Search

Very recently Jain et al. (J. Inequal. Appl. 2022:73, 2022) introduced the concept of multivalued F-contraction with altering distance function and investigated the existence of best proximity points for this class of mappings. In this article we prove that the existence of best proximity points for multivalued F-contraction non-self mappings can be obtained from the corresponding fixed point result for multivalued F-contraction self mappings, and so the main conclusion due to Jain et al. is not a real generalization of fixed point theory. [ABSTRACT FROM AUTHOR]

Recently, Altun et al. [1] introduced the notion of p-proximal contractions and discussed about best proximity point results for this class of mappings. Then Gabeleh and Markin [4] showed that the best proximity point theorem proved by Altun et al. in [1] follows from the fixed point theory. In this short note, we show that if the p-proximal contraction constant k < 1 3 then the existence of best proximity point for p-proximal contractions follows from the celebrated Banach contraction principle. [ABSTRACT FROM AUTHOR]

Very recently I. Beg et al. [I. Beg, A. Bartwal, S. Rawat and R.C. Dimri, Best proximity points in noncommutative Banach spaces, Comp. Appl. Math., 41, 41 (2022)] introduced the concepts of k-ordered proximal contraction of the first kind and k-ordered proximal contraction of the second kind for non-self mappings and investigated the existence of best proximity points for these two classes of mappings. In the current paper, we show that their existence results are straightforward consequences of the same conclusions in fixed point theory. [ABSTRACT FROM AUTHOR]

In this paper, we examine the existence and uniqueness of solutions for a system of the first-order q-difference equations with multi-point and q-integral boundary conditions using various fixed point (fp) theorems. Also, we give two examples to support our results. [ABSTRACT FROM AUTHOR]

This paper focuses on using piecewise derivatives to simulate the dynamic behavior and investigate the crossover effect within the coupled fractional system with delays by dividing the study interval into two subintervals. We establish and prove significant lemmas concerning piecewise derivatives. Furthermore, we extend and develop the necessary conditions for the existence and uniqueness of solutions, while also investigating the Hyers–Ulam stability results of the proposed system. The results are derived using the Banach contraction principle and the Leary–Schauder alternative fixed-point theorem. Additionally, we employ a numerical method based on Newton’s interpolation polynomials to compute approximate solutions for the considered system. Finally, we provide an illustrative example demonstrating our theoretical conclusions’ practical application. [ABSTRACT FROM AUTHOR]

This paper focuses on exploring the existence of solutions for a specific class of FDEs by leveraging fixed point theorem. The equation in question features the Caputo fractional derivative of order 3 < u ˆ ≤ 4 and includes a term Θ (β , Z (β)) alongside boundary conditions. Through the application of a fixed point theorem in appropriate function spaces, we consider nonlocal conditions along with necessary assumptions under which solutions to the given FDE exist. Furthermore, we offer an example to illustrate the results. [ABSTRACT FROM AUTHOR]

Let A and B be two nonempty subsets of a normed space X, and let T : A ∪ B → A ∪ B be a cyclic (resp., noncyclic) mapping. The objective of this paper is to establish weak conditions on T that ensure its relative nonexpansiveness. The idea is to recover the results mentioned in two papers by Matkowski (Banach J. Math. Anal. 2:237–244, 2007; J. Fixed Point Theory Appl. 24:70, 2022), by replacing the nonexpansive mapping f : C → C with a cyclic (resp., noncyclic) relatively nonexpansive mapping to obtain the best proximity pair. Additionally, we provide an application to a functional equation. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new types of contraction mappings named S-Pata-type contraction mapping and Generalized S-Pata-type contraction mapping in the framework of S-metric space. Then, we prove some new fixed-point results for S-Pata-type contraction mappings and Generalized S-Pata-type contraction mappings. To support our results, we provide examples to illustrate our findings and also apply these results to the ordinary differential equation to strengthen our conclusions. [ABSTRACT FROM AUTHOR]

The analysis of stability in functional equations (FEs) within neutrosophic normed spaces is a significant challenge due to the inherent uncertainties and complexities involved. This paper proposes a novel approach to address this challenge, offering a comprehensive framework for investigating stability properties in such contexts. Neutrosophic normed spaces are a generalization of traditional normed spaces that incorporate neutrosophic logic. By providing a systematic methodology for addressing stability concerns in neutrosophic normed spaces, our approach facilitates enhanced understanding and control of complex systems characterized by indeterminacy and uncertainty. The primary focus of this research is to propose a novel class of Euler-Lagrange additive FE and investigate its Ulam-Hyers stability in neutrosophic normed spaces. Direct and fixed point techniques are utilized to achieve the required results. [ABSTRACT FROM AUTHOR]

Recent research indicates the need for improved models of physical phenomena with multiple shocks. One of the newest methods is to use differential inclusions instead of differential equations. In this work, we intend to investigate the existence of solutions for an m-dimensional system of quantum differential inclusions. To ensure the existence of the solution of inclusions, researchers typically rely on the Arzela–Ascoli and Nadler's fixed point theorems. However, we have taken a different approach and utilized the endpoint technique of the fixed point theory to guarantee the solution's existence. This sets us apart from other researchers who have used different methods. For a better understanding of the issue and validation of the results, we presented numerical algorithms, tables, and some figures. The paper ends with an example. [ABSTRACT FROM AUTHOR]

This paper deals with a class of second-order linear differential equations with periodic coefficients. By viable transformation, we put the second-order linear differential equation into Riccati’s equation. By means of two periodic solutions of Riccati’s equation and variable transformation, we obtain the existence and uniqueness of the periodic solution of the nonhomogeneous second-order linear differential equation, some new results are obtained. [ABSTRACT FROM AUTHOR]

The goal of this paper is to develop new fixed points for quasi upper semicontinuous set-valued mappings and compact continuous (single-valued) mappings, and related applications for useful tools in nonlinear analysis by applying the best approximation approach for classes of semiclosed 1-set contractive set-valued mappings in locally p-convex and p-vector spaces for p ∈ (0 , 1 ] . In particular, we first develop general fixed point theorems for quasi upper semicontinuous set-valued and single-valued condensing mappings, which provide answers to the Schauder conjecture in the affirmative way under the setting of locally p-convex spaces and topological vector spaces for p ∈ (0 , 1 ] ; then the best approximation results for quasi upper semicontinuous and 1-set contractive set-valued mappings are established, which are used as tools to establish some new fixed points for nonself quasi upper semicontinuous set-valued mappings with either inward or outward set conditions under various boundary situations. The results established in this paper unify or improve corresponding results in the existing literature for nonlinear analysis, and they would be regarded as the continuation of the related work by Yuan (Fixed Point Theory Algorithms Sci. Eng. 2022:20, 2022)–(Fixed Point Theory Algorithms Sci. Eng. 2022:26, 2022) recently. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of generalized (α , ϕ) -Meir–Keeler hybrid contractive mappings of type I and II via simulation function and establish fixed point theorems for such mappings in the setting of complete b-metric spaces. Our results extend and generalize many related fixed point results in the existing literature. Finally, we provide an example in support of our main finding. [ABSTRACT FROM AUTHOR]

In this paper we introduce and analyze new Banach spaces-based mixed finite element methods for the stationary nonlinear problem arising from the coupling of the convective Brinkman-Forchheimer equations with a double diffusion phenomenon. Besides the velocity and pressure variables, the symmetric stress and the skew-symmetric vorticity tensors are introduced as auxiliary unknowns of the fluid. Thus, the incompressibility condition allows to eliminate the pressure, which, along with the velocity gradient and the shear stress, can be computed afterwards via postprocessing formulae depending on the velocity and the aforementioned new tensors. Regarding the diffusive part of the coupled model, and additionally to the temperature and concentration of the solute, their gradients and pseudoheat/pseudodiffusion vectors are incorporated as further unknowns as well. The resulting mixed variational formulation, settled within a Banach spaces framework, consists of a nonlinear perturbation of, in turn, a nonlinearly perturbed saddle-point scheme, coupled with a usual saddle-point system. A fixed-point strategy, combined with classical and recent solvability results for suitable linearizations of the decoupled problems, including in particular, the Banach-Nečas-Babuška theorem and the Babuška-Brezzi theory, are employed to prove, jointly with the Banach fixed-point theorem, the well-posedness of the continuous and discrete formulations. Both PEERS and AFW elements of order ℓ ⩾ 0 for the fluid variables, and piecewise polynomials of degree ⩽ ℓ together with Raviart-Thomas elements of order ℓ for the unknowns of the diffusion equations, constitute feasible choices for the Galerkin scheme. In turn, optimal a priori error estimates, including those for the postprocessed unknowns, are derived, and corresponding rates of convergence are established. Finally, several numerical experiments confirming the latter and illustrating the good performance of the proposed methods, are reported. [ABSTRACT FROM AUTHOR]

For multiple sensor estimation in nonlinear Gaussian environment, the traditional Gauss-Hermite quadrature information filter (GHQIF) has great performance. However, due to the precision loss caused by rounding errors, GHQIF may cause a series of problems such as system divergence. Therefore, the square root GHQIF (SRGHQIF) is first proposed in this paper; it ensures the symmetry and semipositive quality of covariance matrices, also improves the numerical stability and estimation accuracy. Furthermore, practical systems are usually non-Gaussian, and the GHQIF and SRGHQIF under the minimum mean square error (MMSE) rule both deteriorate seriously in this situation. Therefore, replacing MMSE rule with robust maximum correntropy criterion (MCC) as the optimal criterion, a new information filter called the maximum correntropy SRGHQIF (MCSRGHQIF) is proposed, which can improve the robustness of the SRGHQIF against impulsive noise. The predicted information matrix and vector of the SRGHQIF are calculated and then corrected and reconstructed with the MCC. In addition, fixed-point theory is used to iteratively update the estimation information vector, which can obtain better estimation results. Finally, the target tracking simulation results verify that the MCSRGHQIF is a very effective algorithm for multiple sensor estimation in nonlinear non-Gaussian environment, and the newly proposed MCSRGHQIF retains the frameworks and advantages of the SRGHQIF and MCC. [ABSTRACT FROM AUTHOR]

Compared with classical tuned mass damper (TMD), inerter system has higher damping efficiency and wider vibration control range. The traditional fixed-point theory of TMD have been used in most of the previous optimal parameter designs of inerter system, the optimized parameters obtained are expressed by the inerter-mass ratio, which may not be applicable to some specific inerter systems (such as tuned viscous mass damper, TVMD) or are too cumbersome. In this paper, the optimal parameters of the inerter system based on the characteristics of the grounded element and muti-performances demand are derived, and demand-based global optimal methods of the design parameters of the inerter system are proposed and compared. The correctness, feasibility and applicability of methods are verified by optimization examples and typical excitation including ground motions. The optimal parameters combinations of the inerter system derived based on the grounded element exist unique analytical expressions. When the value of the grounded element and the objective function are determined, the local optimal design of the inerter system can be realized. If the precise displacement vibration control of original structure is needed, the optimal parameters obtained by the stochastic displacement response that is taken as the objective function can be selected. If the demand is that total energy input of original structure requires is minimum, and the requirements for small displacement control effect are not strict, the optimal parameters of the inerter system obtained by the stochastic velocity response can be selected. If it is necessary to minimize the engineering cost and the control the peak and RMS displacement at the mean time, the optimal parameters of the inerter system obtained by deformation enhancement coefficient of damping element can be selected. The analytical expressions of the optimal design parameters of the inerter system based on the grounded element are concise and the processes of optimal design based on multiple performances objectives are simple, which can be applied to a variety of demands in practical engineering. [ABSTRACT FROM AUTHOR]

In this paper we consider a strongly coupled flow and nonlinear transport problem arising in sedimentation-consolidation processes in R n , n ∈ { 2 , 3 } , and introduce and analyze a Banach spaces-based variational formulation yielding a new mixed-primal finite element method for its numerical solution. The governing equations are determined by the coupling of a Brinkman flow with a nonlinear advection–diffusion equation, in addition to Dirichlet boundary conditions for the fluid velocity and the concentration. The approach is based on the introduction of the Cauchy fluid stress and the gradient of its velocity as additional unknowns, thus yielding a mixed formulation in a Banach spaces framework for the Brinkman equations, whereas the usual Hilbertian primal formulation is employed for the transport equation. Differently from previous works on this and related problems, no augmented terms are incorporated, and hence, besides becoming fully equivalent to the original physical model, the resulting variational formulation is much simpler, which constitutes its main advantage, mainly from the computational point of view. The well-posedness of the continuous formulation is analyzed firstly by rewriting it as a fixed-point operator equation, and then by applying the Schauder and Banach theorems, along with the Babuška-Brezzi theory and the Lax-Milgram lemma. An analogue fixed-point strategy is employed for the analysis of the associated Galerkin scheme, using in this case the Brouwer theorem instead of the Schauder one. The resulting discrete scheme becomes momentum conservative for the fluid in an approximate sense. Next, a Strang-type lemma and suitable algebraic manipulations are utilized to derive the a priori error estimates, which, along with the approximation properties of the finite element subspaces, yield the corresponding rates of convergence. The paper is ended with several numerical results illustrating the performance of the mixed-primal scheme and confirming the theoretical decay of the error. [ABSTRACT FROM AUTHOR]

We provide in this paper a numerical iterative approach for solving nonlinear fuzzy integral equations using Newton–Cotes rules (abbreviated NC rules). We show how to employ NC rules and successive approximation sequences to approximate the Urysohn fuzzy integral equation of the second kind. The modulus of continuity will be utilized for demonstrating convergence analysis and error estimation. Finally, we evaluate the efficiency, accuracy, and applicability of theoretical conclusions of our technique in practice examples from reliable references. The errors demonstrate the method's excellent accuracy. [ABSTRACT FROM AUTHOR]

The study of the zero existence problem for a nonnegative set-valued functional on a metric space is continued. The zero existence problem for a functional related by a certain -continuity condition to a parametric family of -search functionals on an open subset of a metric space is examined. A theorem containing several sufficient conditions for this functional to have zeros is proved. As corollaries of this result, theorems on the existence of coincidence and fixed points are also proved for set-valued mappings related by the -continuity condition to families of set-valued mappings with the property that the existence of coincidence and fixed points in an open subset of a metric space is preserved under parameter variation. For uniformly convex metric spaces, analogs of M. Edelstein's 1972 asymptotic center theorem and M. Frigon's 1996 fixed point theorem for nonexpansive mappings of Banach spaces are obtained and compared with the main results of the paper. [ABSTRACT FROM AUTHOR]

In this paper we are concerned with the Common Fixed Point Problem (CFPP) with demi-contractive operators and its special instance, the Convex Feasibility Problem (CFP) in real Hilbert spaces. Motivated by the recent result of Ordoñez et al. [35] and in general, the field of online/real-time algorithms, for example [19, 20, 30], in which the entire input is not available from the beginning and given piece-by-piece, we propose an online/real-time iterative scheme for solving CFPPs and CFPs in which the involved operators/sets emerge along time. This scheme is capable of operating on any block, for any finite number of iterations, before moving, in a serial way, to the next block. The scheme is based on the recent novel result of Reich and Zalas [37] known as the Modular String Averaging (MSA) procedure. The convergence of the scheme follows [37] and other classical results in the fields of fixed point theory and variational inequalities, such as [34]. Numerical experiments for linear and nonlinear feasibility problems with applications to image recovery are presented and demonstrate the validity and potential applicability of our scheme for example to online/real-time scenarios. [ABSTRACT FROM AUTHOR]

Application of the supersymmetric localization method to theories on anti-de Sitter spacetime has received recent interest, yet still remains as a challenging problem. In this paper, we focus on (global) Euclidean AdS2, on which we consider an Abelian 풩 = (2) theory and implement localization computation to obtain the exact partition function. For comparison, we also revisit the theory on S2 and perform a parallel computation. We refine the notion of equivariant supersymmetry and use appropriate functional integration measure. For AdS2 we choose a supersymmetric boundary condition which is compatible with the principle of variation. To evaluate the 1-loop determinant about the localization saddle, we use index theory and fixed point formula, where we pay attention to the effect of zero modes and their superpartners. The existence of fermionic superpartner of 1-form boundary zero modes is proven. Obtaining the 1-loop determinant requires expansion of the index that presents an ambiguity, which we resolve using boundary condition. The resulting partition function reveals an overall dependence on the size of the background manifold, AdS2 as well as S2, as a sum of two types of contributions: a local one from local conformal anomaly through the index computation and a global one coming from zero modes. This overall size dependence matches with the perturbative 1-loop evaluation using heat kernel method. [ABSTRACT FROM AUTHOR]

In this work, the existence and the controllability of impulsive stochastic integro-differential equations with infinite delay are investigated. Unlike previous papers, the result of this one relies upon some weaker assumptions using a recently defined measure of noncompactness, resolvent operator solution in sense of Grimmer and Mönch fixed point theorem. The semigroup is only required to be strongly continuous. At the end, examples are presented to illustrate the obtained result. [ABSTRACT FROM AUTHOR]

This paper is the first to introduce a fixed point problem of integral type in a -metric space. We study sufficient conditions for the existence and uniqueness of a common fixed point of contractive mappings of integral type. We also give two examples to support our results. [ABSTRACT FROM AUTHOR]

A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. It is new for isometries of convex sets of Banach spaces as well as for non-locally compact CAT(0)-spaces and injective spaces. Examples of actions on non-proper CAT(0)-spaces come from the study of diffeomorphism groups, birational transformations, and compact Kähler manifolds. A special case of the fixed point theorem provides a novel mean ergodic theorem that in the Hilbert space case implies von Neumann's theorem. The theorem accommodates classically fixed-point-free isometric maps such as those of Kakutani, Edelstein, Alspach and Prus. Moreover, from the main theorem together with some geometric arguments of independent interest, one can deduce that every bounded invertible operator of a Hilbert space admits a nontrivial invariant metric functional on the space of positive operators. This is a result in the direction of the invariant subspace problem although its full meaning is dependent on a future determination of such metric functionals. [ABSTRACT FROM AUTHOR]

Purpose: This paper propose a grounded-type DVA attached to a damped primary system, which can effectively suppress the vibration amplitudes by introducing a lever, focusing on the optimal design of the novel DVA. It can be utilized to the simplified model of a damped spacecraft or stay cable of cable-stayed bridges. Methods: The design of DVA considers H ∞ and H 2 optimization criteria, and defines performance indicators separately. In the H ∞ optimization, we couple generalized fixed-point theory (GFPT) and perturbation method (PM) with particle swarm optimization (PSO) algorithm to minimize the maximum amplitude amplification factor of primary system, so that the amplitudes at two fixed points are close to the same horizontal line. Nevertheless, in the H 2 optimization, the GFPT and PM are combined with Newton's method to minimize the power input to primary system. Results: The numerical results indicate the consistency and effectiveness of the two optimization criteria. Compared with other classical models, the effects of different grounded stiffness ratios on the amplitude frequency responses, time histories, and vibration energies of the primary system subjected to harmonic excitation and random excitation, respectively, as well as the vibration reduction effect, are studied. Conclusions: Numerical simulations display with the positive grounded stiffness, the proposed DVA outperform the existing DVAs with same mass, damping, and stiffness under the harmonic excitation and random excitation. The results can provide theoretical and computational guidance for the optimal design of DVA. [ABSTRACT FROM AUTHOR]

For any orientable finite-volume hyperbolic 3-manifold, this paper proves that the profinite isomorphism type of the fundamental group uniquely determines the isomorphism type of the first integral cohomology, as marked with the Thurston norm and the fibered classes; moreover, up to finite ambiguity, the profinite isomorphism type determines the isomorphism type of the fundamental group, among the class of finitely generated 3-manifold groups. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the existence and uniqueness of fractional differential equations (FDEs) by using the fixed-point theory (FPT). We discuss also the Ulam–Hyers–Rassias (UHR) stability of some generalized FDEs according to some classical mathematical techniques and the FPT. Finally, two illustrative examples are presented to show the validity of our results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to develop some fundamental and important nonlinear analysis for single-valued mappings under the framework of p-vector spaces, in particular, for locally p-convex spaces for 0 < p ≤ 1 . More precisely, based on the fixed point theorem of single-valued continuous condensing mappings in locally p-convex spaces as the starting point, we first establish best approximation results for (single-valued) continuous condensing mappings, which are then used to develop new results for three classes of nonlinear mappings consisting of 1) condensing; 2) 1-set contractive; and 3) semiclosed 1-set contractive mappings in locally p-convex spaces. Next they are used to establish the general principle for nonlinear alternative, Leray–Schauder alternative, fixed points for nonself mappings with different boundary conditions for nonlinear mappings from locally p-convex spaces, to nonexpansive mappings in uniformly convex Banach spaces, or locally convex spaces with the Opial condition. The results given by this paper not only include the corresponding ones in the existing literature as special cases, but are also expected to be useful tools for the development of new theory in nonlinear functional analysis and applications to the study of related nonlinear problems arising from practice under the general framework of p-vector spaces for 0 < p ≤ 1 . Finally, the work presented by this paper focuses on the development of nonlinear analysis for single-valued (instead of set-valued) mappings for locally p-convex spaces. Essentially, it is indeed the continuation of the associated work given recently by Yuan (Fixed Point Theory Algorithms Sci. Eng. 2022:20, 2022); therein, the attention is given to the study of nonlinear analysis for set-valued mappings in locally p-convex spaces for 0 < p ≤ 1 . [ABSTRACT FROM AUTHOR]

The contraction condition in the Banach contraction principle forces a function to be continuous. Many authors overcome this obligation and weaken the hypotheses via metric spaces endowed with a partial order. In this paper, we present some coupled fixed point theorems for the functions having mixed monotone properties on ordered vector metric spaces, which are more general spaces than partially ordered metric spaces. We also define the double monotone property and investigate the previous results with this property. In the last section, we prove the uniqueness of a coupled fixed point for non-monotone functions. In addition, we present some illustrative examples to emphasize that our results are more general than the ones in the literature. [ABSTRACT FROM AUTHOR]

This paper investigates on the H ∞ and H 2 control performances for a novel grounded inerter-based dynamic vibration absorber configuration (GIDVA) by entirely replacing both damper and stiffness of the classic dynamic vibration absorber with grounded inerter-based mechanical network. First, the equations of motion of the coupled system are derived and the analytical solution is established in terms of primary system displacement under harmonic excitation. Then, the optimum tuning parameters are found by first using the extended fixed points theory (EFPT) to get analytical design. It is found that this EFPT yields the approximate but accurate analytical solutions, so this method can be commonly used to design inerter-based DVAs with four fixed points in the frequency response curves of the primary system. Further, to evaluate the control performance of the proposed GIDVA, the numerical H ∞ and H 2 optimizations are performed in MATLAB for the case of harmonic and random excitation, respectively, using the Newton–Raphson algorithm with the starting points, the analytical approximate optimal parameters based on the EFPT. Based on the results comparison of the control performance, one can remark that with the same small mass ratio, the proposed GIDVA can decrease the peak vibration amplitude of primary system more than 64% and 50% and enlarge the suppression bandwidth more than 64% and 57% when compared with the classic DVA and the recent published non-traditional inerter-based DVAs (NIDVA- C i , i=3, 4, 6), respectively, for both optimal designs H ∞ and H 2 . However, one can also notice that this improvement decreases with the increase in the mass ratio. Moreover, under random excitation, the GIDVA also shows good control performance with 56% and 44% reduction in terms of mean square and time history responses of primary system. This result reveals the potential of a novel grounded inerter-based dynamic vibration absorber, which provides a reference for the design index of the novel vibration absorber in engineering practice. [ABSTRACT FROM AUTHOR]

In this paper, we consider the nonhomogeneous fractional delay oscillation equation with order κ and investigate the existence of a unique solution in matrix-valued fuzzy Banach spaces for this equation using the alternative fixed point theorem. In a fuzzy environment, we introduce a class of the matrix-valued fuzzy Wright controller to investigate the Hyers–Ulam–Wright stability for the NH-FD-O equation with order κ. Finally, an illustrative example to demonstrate the application of the main theorem is also considered. [ABSTRACT FROM AUTHOR]

In this paper, a numerical technique is developed for the solution of multi-term fractional differential equations (FDEs) upto fourth order by using Haar collocation method (HCM). In Caputo sense, the fractional derivative is defined. The integral involved in the equations is calculated by the method of Lepik. The HCM converts the given multi-term FDEs into a system of linear equations. The convergence of the proposed method HCM is checked on some problems. Mean square root and maximum absolute errors are calculated for different numbers of collocation points(CPs), which are recorded in tables. The exact and approximate solution comparison is also given in figures. The time taken by CPU for numerical results is also given in the tables. [ABSTRACT FROM AUTHOR]

The foremost goal of this paper is to study the sufficient conditions for controllability of Hilfer fractional Langevin dynamical system with impulse. The main results are obtained by using the generalized fractional calculus and fixed point theory. Finally, a pair of examples are equipped to demonstrate the importance of the obtained theoretical result. The homotopy perturbation method (HPM) is successfully used in the numerical example. [ABSTRACT FROM AUTHOR]

In this paper we consider the system of partial differential equations describing the stress-assisted diffusion of a solute into an elastic material, and introduce and analyze a Banach spaces-based variational approach yielding a new mixed-primal finite element method for its numerical solution. The elasticity model involved, which is initially defined according to the constitutive relation given by Hooke’s law, and whose momentum equation holds with a concentration-depending source term, is reformulated by using the non-symmetric pseudostress tensor and the displacement as the only unknowns of the associated mixed scheme, in addition to assuming a Dirichlet boundary condition for the latter. In turn, the diffusion equation, whose diffusivity function and source term depend on the stress and the displacement of the solid, respectively, is set in primal form in terms of the concentration unknown and a Dirichlet boundary condition for it as well. The resulting coupled formulation is rewritten as an equivalent fixed point operator equation, so that its unique solvability is established by employing the classical Banach theorem along with the corresponding Babuška-Brezzi theory and the Lax-Milgram theorem. The aforementioned dependence of the diffusion coefficient and the subsequent treatment of this term in the continuous analysis, suggest to better look for the solid unknowns in suitable Lebesgue spaces. The discrete analysis is performed similarly, and the Brouwer theorem yields existence of a Galerkin solution. A priori error estimates are derived, and rates of convergence for specific finite element subspaces satisfying the required discrete inf-sup conditions, are established in 2D. Finally, several numerical examples illustrating the performance of the method and confirming the theoretical convergence, are reported. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove some new fixed point results for a pair of multivalued dominated locally contractive mappings in b-multiplicative metric space. Further, fixed point theorems for multigraph-dominated mappings are also established. Some new fixed point results on a closed ball are obtained for a pair of multigraph-dominated mappings endowed with graphic structure in b-multiplicative metric space. An illustrative example is given to show the validity of the hypothesis of our obtained result. Moreover, applications for a coupled system of nonlinear Volterra-type integral equations and functional equations in dynamic programming are presented to show the novelty of our results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some best proximity point results on 0-complete partial metric spaces by introducing a new concept of mixed multivalued contraction mapping. Thus, we generalize and extend some important and famous results existing in the literature. To support our results, we present a noteworthy illustrative and comparative example. Finally, we give some applications of our new best proximity point theorems to homotopy theory as directly unlike homotopy applications existing in the literature. Hence, we prove some best proximity point results for homotopic mappings. [ABSTRACT FROM AUTHOR]

In this paper, we have established some fixed point theorems in the context of strong b-metric spaces. For this purpose, Ciric type contraction for single-valued mapping and Nadler's type Banach and Chatterjea contractions for set-valued mappings are applied to obtain fixed point and common fixed points. A simple and different technique has been used to obtain the results. Our results unify, extend and generalize the existence of corresponding present and conventional results existing in the literature of fixed point theory. [ABSTRACT FROM AUTHOR]

The goal of this research is to find a solution for controlling influenza evolution and its transmission. In the present paper, a new time-dependent nonlinear susceptible–infected–recovered–cross-immune model is introduced with arbitrary order Atangana–Baleanu derivative, and its solution is found using the reliable hybrid computational technique known as homotopy perturbation method via Laplace transform. The arbitrary order derivative is taken in the Liouville–Caputo sense. The outcomes of different parameters on various populations with time are displayed through graphical results. The existence and uniqueness of the solution of the presented model is discussed using Picard–Lindelof approach. Convergence analysis is also shown. The negligible error in the succeeding iterates shows the accuracy of the homotopy perturbation transform method (HPTM) scheme. The plots and the obtained results show activeness, effectiveness and suitability of HPTM scheme in solving this fractional model. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of control functions, namely extended FZ -simulation functions, and employ it to define a new contractive condition. We also prove some new fixed and best proximity point results in the context of an M-complete fuzzy metric space. The presented theorems unify, generalize, and improve several existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of generalized quasimetric spaces by a new approach, and present some examples in the partial metric spaces. Furthermore, we obtain some results on (strong) complete partial metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we incorporate proximal point algorithm with some convex combination techniques to approximate a minimizer and a common fixed point of a family of multi-valued mappings in Hadamard spaces. We prove -convergence and strong convergence theorems for a convex lower semi-continuous function and multi-valued quasi-nonexpansive mappings. Furthermore, we apply our results to find mean, median and solve equilibrium problems in Hadamard spaces. Finally, we give two numerical examples, one in a non-Hilbert space with a non-convex functional and the other in a Hilbert space, to demonstrate the convergence of the proposed method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the existence of mild solutions and approximate controllability for measure driven evolution system with nonlocal conditions. First, we obtain the existence of mild solutions and approximate controllability for the concerned problem by constructing new Green's function and control function involving Gramian controllability operator. This research relies on Schauder's fixed point theorem and the theory of operator semigroup. At the end, two examples are also given to illustrate the feasibility of our theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we investigate an norovirus (NoV) epidemic model with stochastic perturbation and the new definition of a nonlocal fractal–fractional derivative in the Atangana–Baleanu–Caputo (ABC) sense. First we present some basic properties including equilibria and the basic reproduction number of the model. Further, we analyze that the proposed stochastic system has a unique global positive solution. Next, the sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established. Furthermore, the fractal–fractional dynamics of the proposed model under Atangana–Baleanu–Caputo (ABC) derivative of fractional order " p " and fractal dimension " q " have also been addressed. Besides, coupling the non-linear functional analysis with fixed point theory, the qualitative analysis of the proposed model has been performed. The numerical simulations are carried out to demonstrate the analytical results. It is believed that this study will comprehensively strengthen the theoretical basis for comprehending the dynamics of the worldwide contagious diseases. [ABSTRACT FROM AUTHOR]

In this paper, we propose the notion of (ψ , ϕ) -Wardowski contraction pairs and achieve a common fixed point theorem consistent with such kind of contractions in complete metric spaces. One of the main motivations of this article is to define a contractive condition which does not compel the mappings to be continuous at their common fixed points, an interesting question posed by Rhoades (Contemporary Math 72:233–245, 1988). Besides, we provide some applications of our obtained results in certain type of operator equations, fractional differential equation boundary value problems, functional equations arising in dynamic programmings, and a particular type of non-linear quadratic integral equations which are relevant to events arising in physics, economics, engineering, operations research, and many other relevant disciplines. [ABSTRACT FROM AUTHOR]

The paper deals with the existence, oscillation, and nonoscillation of solutions to some classes of Caputo fractional q-difference equations and inclusions. The technique of proving employs set-valued analysis, fixed-point theory, and the method of upper and lower solutions. [ABSTRACT FROM AUTHOR]

In this paper, we derive some common α-fuzzy fixed point results for fuzzy mappings under generalized almost F -contractions in the context of a controlled metric space, which generalize many preexisting results in the literature. As an application, we establish some multivalued fixed point results. For justification of our results, we provide a nontrivial example. [ABSTRACT FROM AUTHOR]

In this paper, we study the uniqueness and existence of the solution of a non-autonomous and nonsingular delay difference equation using the well-known principle of contraction from fixed point theory. Furthermore, we study the Hyers–Ulam stability of the given system on a bounded discrete interval and then on an unbounded interval. An example is also given at the end to illustrate the theoretical work. [ABSTRACT FROM AUTHOR]

The aim of this study is to introduce a new interpolative contractive mapping combining the Hardy–Rogers contractive mapping of Suzuki type and Z -contraction. We investigate the existence of a fixed point of this type of mappings and prove some corollaries. The new results of the paper generalize a number of existing results which were published in the last two decades. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of algebras satisfying certain conditions which has been named power algebras and we prove some fixed point theorems for a new class of contractions. We give new conditions for the existence and uniqueness of fixed points for this new class of mappings which are not a contraction in the usual algebra. Also, we introduce a new iterative algorithm for fixed-point problems in a Banach algebra. This results improve and extend the corresponding conclusions of the Ishikawa algorithm under weaker conditions and lead to stronger results. In conclusion, we give an application to nonlinear integral equations. [ABSTRACT FROM AUTHOR]

In the present work, we investigate infinite horizon optimal control problems driven by a class of stochastic delay evolution equations in Hilbert spaces and the corresponding adjoint equation is given by an anticipated backward stochastic evolution equation (ABSEE). We first establish a priori estimate for the solution to ABSEEs by imposing restriction on unbounded operator A ∗ , that is, the operator A ∗ is maximal dissipative. In this way, the Itô inequality is applicable in our study, and we can also avoid the problem that neither Itô formula nor energy equation is available. Next, we obtain the existence and uniqueness results of solutions of linear backward stochastic evolution equations on infinite horizon by using approximating methods. Then, the existence and uniqueness results of ABSEEs on infinite horizon is obtained via the fixed-point theory. That is the highlight of innovation in this paper. Eventually, we establish necessary and sufficient conditions for optimality of the control problem on infinite horizon, in the form of Pontryagin's maximum principle. [ABSTRACT FROM AUTHOR]