Search

In this paper, we introduce a new class of metric spaces called the Menger probabilistic bipolar metric space and define some other notions related to this space. Moreover, we prove some uniqueness fixed point theorems for two cases including the covariant and contravariant maps. These fixed point theorems are new versions of the Banach contraction principle, Kannan theorem, and Reich-type theorem in the context of the Menger probabilistic bipolar metric space. Throughout the paper, we provide some examples to understand the definitions in the better manner. Finally, two applications are given for proving the uniqueness result in the form of an integral equation and a fractional boundary value problem. [ABSTRACT FROM AUTHOR]

The aim of this paper is to exhibit a novel two-step iterative algorithm named PV algorithm to determine the fixed points of weak contractions in Banach spaces. Data dependence result is also obtained. It is proved that this PV iterative algorithm converges strongly to the fixed point of weak contractions. This iteration is almost stable for weak contraction. Furthermore, it is proved that rate of convergence of the PV iterative algorithm is faster than Picard, Ishikawa, Mann, S,normal-S, Varat, and F* algorithms. Examples are also given to support the main result. The results of this paper are original and will further enrich the existing literature. [ABSTRACT FROM AUTHOR]

This paper provides an iterative construction for a common solution associated with the pseudomonotone equilibrium problems, fixed point problem of a finite family η -demimetric operators and the generalized split null point problem in Hilbert spaces. The sequence of approximants is a variant of the parallel shrinking extragradient algorithm with the inertial effect converging strongly to the optimal common solution under suitable set of control conditions. The viability of the approximants is demonstrated for various theoretical as well as numerical results. The results presented in this paper improve various existing results in the current literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new Bregman extragradient method with a different line-search process for solving variational inequality problems in reflexive Banach spaces. Precisely, we prove that the sequence generated by our proposed iterative algorithm converges strongly to an element of the solution sets of variational inequality problems. Moreover, some numerical examples are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a (p , q) -fractional nonlinear difference equation of different orders is considered and discussed. With the help of (p , q) -calculus for integrals and derivatives properties, we convert the main integral boundary value problem (IBVP) to an equivalent solution in the form of an integral equation, we use the upper–lower solution technique to prove the existence of positive solutions. We present an example of the IBVP to apply and demonstrate the results of our method. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results for a pair of relatively nonexpansive mappings using Thakur iteration in uniformly convex W-hyperbolic spaces. Our results extend some of the existing results in the literature. We illustrate the results with an example. Also, we compare the convergence of two different types of Thakur iterations for a pair of relatively nonexpansive mappings and establish that one converges faster than the other. We also establish the existence of a best proximity pair using the main theorem. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of unified interpolative contractions of the Reich–Rus–Ćirić type and give some results about the fixed points for these mappings in the framework of relational metric spaces. We present examples where the results of some previous research are not relevant. Also, we apply our results to solving problems related to nonlinear matrix equations, emphasizing their practical importance. [ABSTRACT FROM AUTHOR]

The primary focus of this paper is threefold: first, to investigate the existence of mild solutions; second, to analyze the topological and geometrical structure of the solution sets; and third, to determine the continuous dependence of the solution for second-order semilinear integro-differential inclusion. In this study, we employ Bohnenblust–Karlin’s fixed point theorem in conjunction with the theory of resolvent operators, as presented by Grimmer. An illustrative example is employed to showcase the achieved outcomes. [ABSTRACT FROM AUTHOR]

The notion of A -condensing operators via the measure of noncompactness is proposed, which retains the existing classes of condensing operators. Results concerning the existence of the best proximity point (pair) of cyclic (noncyclic) A -condensing operators along with the coupled best proximity-point theorem for cyclic A -condensing operators have been formulated. An application to a (k , ℷ) -Hilfer fractional differential equation of order 2 < p < 3 , type q ∈ [ 0 , 1 ] satistfying some boundary conditions is presented. The paper is the first to investigate the optimum solution of such a generalized fractional differential equation. The hypothesis involved in the investigation is independent of the incorporated measure of noncompactness, thereby making our result better in application than that present in the literature. Moreover, added numerical examples validate the theoretical conclusions. [ABSTRACT FROM AUTHOR]

In this paper, an inertial subgradient extragradient algorithm is proposed to solve the pseudomonotone variational inequality problems in Banach space. This iterative scheme employs a new line-search rule. Strong convergence theorems for the proposed algorithms are established under the assumptions that the operators are non-Lipschitz continuous. Furthermore, several numerical experiments are given to show that our method has better convergence performance than the known ones in the literatures. [ABSTRACT FROM AUTHOR]

The aim of this paper is to discuss some results concerning the demiclosedness principle of generalized, nonexpansive mappings in uniformly convex spaces. Further, we present some new fixed-point theorems for generalized nonexpansive mappings in different settings of Banach spaces. [ABSTRACT FROM AUTHOR]

This paper proposes a new inertial subgradient extragradient method for solving equilibrium problems with pseudomonotone and Lipschitz-type bifunctions and fixed point problems for nonexpansive mappings in real Hilbert spaces. Precisely, we prove that the sequence generated by proposed algorithm converges strongly to a common solution of equilibrium problems and fixed point problems. We use an effective self-adaptive step size rule to accelerate the convergence process of our proposed iterative algorithm. Moreover, some numerical results are given to show the effectiveness of the proposed algorithm. The results obtained in this paper extend and improve many recent ones in the literature. [ABSTRACT FROM AUTHOR]

Modeling dynamical systems with real-life data having time-dependent disturbances is better captured with time-varying systems. The qualitative properties of such a system in a fractional sense are hardly examined. Observability is one property where the system's initial states are determined based on the output of some observation system. In this paper, we investigate the observability of time-varying fractional dynamical systems. A state-transition matrix represents the solution of the time-varying fractional dynamical systems. The observability results of linear and nonlinear systems are obtained using the Gramian matrix technique and the Banach contraction mapping theorem respectively. The obtained theoretical results for the observability of the time-varying fractional dynamical systems are compared with those of the time-invariant fractional dynamical system (FDS). Several numerical examples are provided to validate the theoretical results. Also, a numerical example to study the observability of a fractional spring–mass system is provided to verify the applicability of this study. [ABSTRACT FROM AUTHOR]

This paper attempts to investigate the existence of at least one positive solution and the existence of a unique positive solution to an iterative and conformable fractional system associated with the Sturm–Liouville type conditions. The approach employed in this work relies on the well-known Guo–Krasnosel'skii fixed point theorem and Wardowski fixed point theorem. To ensure the validity of our key findings, examples are included. [ABSTRACT FROM AUTHOR]

In this paper, we suggest and analyze four inertial algorithms for solving fixed point problems of Bregman quasi-nonexpansive mappings in the framework of reflexive Banach spaces. Our first two algorithms, we propose inertial-like methods based on Mann-type and Halpern-type iterations, and in the others, we propose relaxed inertial-like methods based on Mann-type and Halpern-type iterations. The weak and strong convergence of the algorithms are established under some appropriate conditions on the parameters. As an application, we utilize our main results to find a zero of the sum of Bregman inverse strongly monotone mappings and maximal monotone operators in real reflexive Banach spaces. Also, we provide several numerical experiments to show the convergence behaviour of our algorithms in both finite-dimensional and infinite-dimensional spaces. Finally, we further utilize our algorithms to numerically solve the data classification problems of lung cancer. [ABSTRACT FROM AUTHOR]

For any fixed s ∈ z ∈ C : z ≠ 0 and | z | < 1 , we consider the following functional inequality: 1 ‖ f (a + a ′ , c + c ′) + f (a + a ′ , c - c ′) + f (a - a ′ , c + c ′) + f (a - a ′ , c - c ′) - 4 f (a , c) - 4 f (a , c ′) ‖ ≤ ‖ s (2 f a + a ′ , c - c ′ + 2 f a - a ′ , c + c ′ - 4 f (a , c) - 4 f (a , c ′) + 4 f (a ′ , c ′)) ‖. In this paper, we obtain the Hyers–Ulam stability of the proposed functional inequality using the direct and fixed point methods. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce two inertial hybrid iteration processes for finding common fixed points of two asymptotically quasi G- ϕ -nonexpansive mappings in uniformly convex and uniformly smooth Banach spaces with directed graphs. After that, we prove some strong convergence results for such iteration processes under suitable assumptions. By these theorems, we obtain some strong convergence results for two quasi G- ϕ -nonexpansive mappings in uniformly convex and uniformly smooth Banach space with directed graphs, and some convergence results in Hilbert spaces with directed graphs. In addition, we give some numerical examples to illustrate the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we propose two new self-adaptive relaxed CQ algorithms to solve the split feasibility problem with multiple output sets, which involve the computation of projections onto half-spaces instead of the computation onto the closed convex sets. Our proposed algorithms with selection technique reduce the computation of projections. And then, as a generalization, we construct two new algorithms to solve the variational inequalities over the solution set of split feasibility problem with multiple output sets. More importantly, strong convergence of all proposed algorithms is proved under suitable conditions. Finally, we conduct numerical experiments to show the efficiency and accuracy of our algorithms compared to some existing results. [ABSTRACT FROM AUTHOR]

This paper introduces an innovative inertial simultaneous cyclic iterative algorithm designed to address a range of mathematical problems within the realm of split equality variational inequalities. Specifically, the algorithm accommodates finite families of split equality variational inequality problems, infinite families of split equality variational inclusion problems, and multiple-sets split equality fixed point problems involving demicontractive operators in infinite-dimensional Hilbert spaces. The algorithm integrates well-established methods, including the cyclic method, the inertial method, the viscosity approximation method, and the projection method. We establish the strong convergence of this proposed algorithm, demonstrating its applicability in various scenarios and unifying disparate findings from existing literature. Additionally, a numerical example is presented to validate the primary convergence theorem. [ABSTRACT FROM AUTHOR]

Our study in this paper is focused on the split equality fixed-point problem with firmly quasi-non-expansive operators in infinite-dimensional Hilbert spaces. A self-adaptive simultaneous scheme is introduced, and its weak convergence is established under mild and standard assumptions. The new proposed scheme generalizes and extends some related works in the literature, and its simple structure makes it easy for implementation and numerical testing. Primary experiments presented in this paper, in finite- and infinite-dimensional spaces, emphasize their practical advantages over existing results. [ABSTRACT FROM AUTHOR]

In this paper, we prove global-in-time existence of strong solutions to a class of fractional parabolic reaction–diffusion systems posed in a bounded domain of R N . The nonlinear reactive terms are assumed to satisfy natural structure conditions which provide nonnegativity of the solutions and uniform control of the total mass. The diffusion operators are of type u i ↦ d i (- Δ) s u i where 0 < s < 1 . Global existence of strong solutions is proved under the assumption that the nonlinearities are at most of polynomial growth. Our results extend previous results obtained when the diffusion operators are of type u i ↦ - d i Δ u i . On the other hand, we use numerical simulations to examine the global existence of solutions to systems with exponentially growing right-hand sides, which remains so far an open theoretical question even in the case s = 1 . [ABSTRACT FROM AUTHOR]

In this paper we study the existence and properties of solutions for a discontinuous sweeping process involving prox-regular sets in a Hilbert spaces. The variation of the moving set is controlled by a positive Radon measure and the perturbation is the sum of two multivalued mappings. The values of the first one are closed, bounded, not necessarily convex sets. It is measurable in the time variable, Lipschitz continuous in the phase variable, and it satisfies a conventional growth condition. The values of the second one are closed, convex, not necessarily bounded sets. We assume that this mapping has a closed with respect to the phase variable graph. Other assumptions concern the intersection of the second mapping with the multivalued mapping defined by the growth conditions. We suppose that this intersection has a measurable selector and it possesses some compactness properties. We prove the existence of right-continuous solutions of bounded variation for our inclusion. If the values of the first inclusion are closed convex sets, then the solution set is a closed subset of the space of right-continuous functions of bounded variation with sup-norm. If, in addition, the values of the moving sets are compact sets, then the solution set is compact in the space of right-continuous functions of bounded variation endowed with the topology of uniform convergence on an interval. The proofs are based on the author’s theorem on continuous with respect to a parameter selectors passing through fixed points of contraction multivalued maps with closed, nonconvex, decomposable values depending on the parameter and some compactness criteria (an analog of the Arzelà–Ascoli theorem) for sets in the space of right-continuous functions of bounded variation with sup-norm. The classical Ky Fan fixed point theorem is also used. The results that we obtain are new. [ABSTRACT FROM AUTHOR]

The paper presents an abstract theory regarding the problems with semilinear operator equations involving iterates of a strongly monotone symmetric linear operator. We obtain existence and localization results of positive solutions for such problems using Krasnosel'skiĭ's technique and abstract Harnack inequality. In particular, we obtain results for problems with semilinear poly-Laplace operators. [ABSTRACT FROM AUTHOR]

In this paper, we prove some generalizations of Darbo’s fixed point theorem for multivalued mappings by considering a measure of noncompactness which does not necessarily have the maximum property. Moreover, we prove some coupled fixed point theorems for multivalued mappings. Our results generalize, prove and extend well-known results in the subject. An application to solve a nonlinear system of integral inclusions is given. [ABSTRACT FROM AUTHOR]

In this paper, we solve the system of functional equations { f (x + y) + g (y − x) = 2 f (x) , g (x + y) − f (y − x) = 2 g (y) and we investigate the stability of g-derivations in Banach algebras. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two types of weak enriched contractions, namely weak enriched F -contraction, weak enriched F ′ -contraction, and k-fold averaged mapping based on Kirk's iterative algorithm of order k. The types of contractions introduced herein unify, extend, and generalize several existing classes of enriched and weak enriched contraction mappings. Moreover, K-fold averaged mappings can be viewed as a generalization of the averaged mappings and double averaged mappings. We then prove the existence of a unique fixed point of the k-fold averaged mapping associated with weak enriched contractions introduced herein. We study necessary conditions that guarantee the equality of the sets of fixed points of the k-fold averaged mapping and weak enriched contractions. We show that an appropriate Kirk's iterative algorithm can be used to approximate a fixed point of a k-fold averaged mapping and of the two weak enriched contractions. We also study the well-posedness, limit shadowing property, and Ulam–Hyers stability of the k-fold averaged mapping. We provide necessary conditions that ensure the periodic point property of each illustrated weak enriched contraction. Some examples are presented to show that our results are a potential generalization of the comparable results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we initiate the fixed point theorems for an orthogonal hybrid interpolative Riech Istrastescus type contractions map on orthogonal b-metric spaces to modify this class proficiently. Also, we provide some examples supporting our main results. Finally, we provide an application to solve the existence and uniqueness of an integral equation with numeric results, which is powerful in a greater way. [ABSTRACT FROM AUTHOR]

This paper considers a first-order nonlinear differential equation that driven by feedback dominated by time delays. Sufficient conditions which determine the number of positive periodic solutions are studied. Our findings give insight into the existence of positive periodic solutions by exploring the Δ -points and ∇ -points that are specifically defined. Moreover, a numerical example and its simulations are provided to illustrate our main results. In this example, at least four positive periodic solutions are ensured by our results. The existence regions of these four positive periodic solutions are also clarified. Finally, we discuss the hematopoietic process (the production process of blood cells) to demonstrate the application of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of Hadamard 픇-hom-der on Banach algebras. Further, we apply the fixed point method to prove the stability of the Hadamard 픇-hom-der on Banach algebras. [ABSTRACT FROM AUTHOR]

Our main focus of this study is based on modified variational inclusion problems with mixed equilibrium problems in real Hilbert space. An iterative algorithm which is the combination of inertial technique and subgradient extragradient algorithm is presented, and under some reasonable assumptions on the control parameters, the strong convergence theorem of the suggested algorithm is proved. In addition, the efficiency of our suggested algorithm is established by a numerical example. The algorithm and analysis provided in this paper are new and generalize some related results in this regard. [ABSTRACT FROM AUTHOR]