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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 note, we give affirmative answers to two open problems posed by Agarwal et al. in the paper (J Optim Theory Appl 163(2):482-490, ). [ABSTRACT FROM AUTHOR]

We show that the result on cyclic weak contractions of Harjani et al. (J. Nonlinear Sci. Appl. 6:279-284, ) holds without the assumption of compactness of the underlying space, and also without the assumption of continuity of the given mapping. [ABSTRACT FROM AUTHOR]

In this note, a small gap is corrected in the assumption of main theorem of T.M. Tuyen (Theorem 3.1, Regularization proximal point algorithm for common fixed points of nonexpansive mappings in Banach spaces, J. Optim. Theory Appl., 152:351-365, ). We give another assumption, which allows us to obtain the strong convergence of regularization algorithms. [ABSTRACT FROM AUTHOR]

In [1] Kohli and Vashistha gave an analogue of probabilistic version of Pant's Theorem ([2], Theorem 1). We note that mappings defined in Examples 3.6 to 3.8 of [1] are not self maps as claimed in the Definitions 3.1 and 3.2. In this context, we provide some relevant examples to complete the interesting results. [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]

In the literature there are several methods for comparing two convergent iterative processes for the same problem. In this note we have in view mostly the one introduced by Berinde in (Fixed Point Theory Appl. 2:97–105, 2004) because it seems to be very successful. In fact, if IP1 and IP2 are two iterative processes converging to the same element, then IP1 is faster than IP2 in the sense of Berinde. The aim of this note is to prove this almost obvious assertion and to discuss briefly several papers that cite the mentioned Berinde's paper and use his method for comparing iterative processes. [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]

The purpose of this paper is to propose an algorithm for solving the split common fixed point problem for strict quasi-ϕ-pseudocontractive mappings in Banach spaces. It is proved that the sequence generated by the proposed iterative algorithm converges strongly to a solution of the split common fixed point problem. Then, the main result is used to study the split common null point problem and the split quasi-inclusion problem. Finally, a numerical example is provided to illustrate our main result. The results presented in this paper extend and improve some recent corresponding results. [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 problem of l2-l∞ stability and disturbance attenuation performance analysis of fixed-point state-space digital filters with external disturbance and finite wordlength nonlinearities is studied in this paper. The finite wordlength nonlinearities are composite nonlinearities representing concatenations of quantization and overflow correction employed in practice. Using sector-based characterization of the finite wordlength nonlinearities, a new l2-l∞ stability criterion for the reduction of the effects of external disturbance to a given level and to confirm the nonexistence of limit cycles in the absence of external interference is established. Numerical examples are given to illustrate the efficacy of the proposed criterion. [ABSTRACT FROM AUTHOR]

The paper concerns with an inertial-like algorithm for approximating solutions of equilibrium problems in Hilbert spaces. The algorithm is a combination around the relaxed proximal point method, inertial effect and the Krasnoselski-Mann iteration. The using of the proximal point method with relaxations has allowed us a more flexibility in practical computations. The inertial extrapolation term incorporated in the resulting algorithm is intended to speed up convergence properties. The main convergence result is established under mild conditions imposed on bifunctions and control parameters. Several numerical examples are implemented to support the established convergence result and also to show the computational advantage of our proposed algorithm over other well known algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study a new kind of nonlocal boundary value problems of nonlinear fractional differential equations supplemented with Erdélyi-Kober type fractional integral conditions. The uniqueness of solutions for the given problem is established by means of contraction mapping principle. Applying nonlinear alternative for contractive maps, we investigate the inclusions case of the problem at hand. Examples illustrating the main results are constructed as well. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study a modified multi-step Noor iterative procedure with errors for two Lipschitz strictly hemicontractive-type mappings in arbitrary Banach spaces and constitute its convergence and stability. The obtained results in this paper generalize and extend the corresponding result of Hussain et al. (Fixed Point Theory Appl. 2012:160, 2012) and some analogous results of several authors in the literature. Finally, a numerical example is included to illustrate our analytical results and to display the efficiency of our proposed novel iterative procedure with errors. [ABSTRACT FROM AUTHOR]

In this paper, a general class of Clifford-valued neutral high-order neural network (HNN) with D-operator on time scales is investigated. In this model, time-varying delays and continuously distributed delays are taken into account. As an extension of the real-valued neural network, the Clifford-valued neural network, which includes a familiar complex-valued neural network and a quaternion-valued neural network as special cases, has been an active research field recently. By utilizing this novel method, which incorporates the differential inequality techniques and the fixed point theorem and time-scale theory of computation, we derive a few sufficient conditions to ensure the existence, uniqueness, and exponential stability of the pseudo almost periodic (PAP) solution of the considered model. The results in this paper are new, even if time scale T = R or T = Z , and complementary to the previously existing works. Furthermore, an example and its numerical simulations are included to demonstrate the validity and advantage of the obtained results. [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]

In this paper, we employ the well-known Krasnoselskii fixed point theorem to study the existence and n-multiplicity of positive periodic solutions for the periodic impulsive functional differential equations with two parameters. The form including an impulsive term of the equations in this paper is rather general and incorporates as special cases various problems which have been studied extensively in the literature. Easily verifiable sufficient criteria are obtained for the existence and n-multiplicity of positive periodic solutions of the impulsive functional differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we propose an iterative algorithm to find the common element of set of solutions of a split equilibrium problem and set of fixed points of an asymptotically nonexpansive mapping in Hilbert spaces. The new method is used to prove the strong convergence for the result of this paper. The result extends the corresponding one in the literature. [ABSTRACT FROM AUTHOR]

Lower semi-continuity from above or upper semi-continuity from below has been used by many authors in recent papers. In this paper, we first study the weak semi-continuity for vector functions having particular form as that of Browder in ordered normed vector spaces; we obtain several new results on the lower semi-continuity from above or upper semi-continuity from below for these vector functions. Our results generalize some well-known results of Browder in scalar case. Secondly, we study the minimum or maximum problems for vector functions satisfying lower semi-continuous from above or upper semi-continuous from below conditions; several new results on the existence of minimal points or maximal points are obtained. We also use these results to study vector equilibrium problems and von Neumann’s minimax principle in ordered normed vector spaces. [ABSTRACT FROM AUTHOR]

This paper addresses the multistability problem for the complex-valued neural networks with appropriate real-imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of fractional semilinear integro-differential equations of order β ∈ (1,2] with nonlocal conditions. By using the solution operator, measure of noncompactness and some fixed point theorems, we obtain the existence of local and global mild solutions for the problem. The results presented in this paper improve and generalize many classical results. An example about fractional partial differential equations is given to show the application of our theory. [ABSTRACT FROM AUTHOR]