Sufficient conditions to solve two systems of integral equations via fixed point results

Abstract The purpose of this paper is to study the solution of two systems of nonlinear integral equations via fixed point results in a complete dislocated b-metric space. Also the notion of graphic contractions on a closed set for two families of graph dominated multivalued mappings is introduced. Our results generalize some previous results in the existing literature

Fixed point results for a pair of fuzzy mappings and related applications in b-metric like spaces

AbstractThis paper is devoted to finding out some realization of the concept of b-metric like space. First, we attain a fixed point for two fuzzy mappings satisfying a suitable requirement of contractiveness. Subsequently, we apply such a result to graphic contractions. Also, we attain a unique solution for a system of integral equations, and lastly we give an application to ensure that there exists a common bounded solution of a suitable functional equation in dynamic programming

Multivalued Fixed Point Results for Two Families of Mappings in Modular-Like Metric Spaces with Applications

The aim of this research work is to find out some results in fixed point theory for a pair of families of multivalued mappings fulfilling a new type of U-contractions in modular-like metric spaces. Some new results in graph theory for multigraph-dominated contractions in modular-like metric spaces are developed. An application has been presented to ensure the uniqueness and existence of a solution of families of nonlinear integral equationsThe authors thank the Basque Government for supporting this work through Grant IT1207-19

Fixed Point Approaches for Multi-Valued Prešić Multi-Step Iterative Mappings with Applications

The purpose of this paper is to present some fixed point approaches for multi-valued Prešić k-step iterative-type mappings on a metric space. Furthermore, some corollaries are obtained to unify and extend many symmetrical results in the literature. Moreover, two examples are provided to support the main result. Ultimately, as potential applications, some contributions of integral type are investigated and the existence of a solution to the second-order boundary value problem (BVP) is presented.This work was supported in part by the Basque Government under grant IT1555-22

Hybrid Ćirić Type Graphic Υ,Λ-Contraction Mappings with Applications to Electric Circuit and Fractional Differential Equations

In this paper, we initiate the notion of Ćirić type rational graphic (Υ,Λ) -contraction pair mappings and provide some new related common fixed point results on partial b-metric spaces endowed with a directed graph G. We also give examples to illustrate our main results. Moreover, we present some applications on electric circuit equations and fractional differential equations.Basque Government through grant IT1207/19

ULAM TYPE STABILITY FOR A CLASS OF SECOND ORDER NONLINEAR DIFFERENTIAL EQUATIONS

In this paper, we are concerned with the stability problem of a general class of second order nonlinear differential equations in the sense of Hyers-Ulam-Rassias and Hyers-Ulam. In our proofs, we show that some of the common restrictions widely used in well-known papers concerned with similar problems on bounded intervals are unnecessary. Therefore, we obtain stability results for second order differential equations with few assumptions on bounded intervals

Generalized Cyclic p-Contractions and p-Contraction Pairs Some Properties of Asymptotic Regularity Best Proximity Points, Fixed Points

This paper studies a general p-contractive condition of a self-mapping T on X, where (X ,d) is either a metric space or a dislocated metric space, which combines the contribution to the upper-bound of d(Tx , Ty), where x and y are arbitrary elements in X of a weighted combination of the distances d(x,y) , d(x,Tx),d(y,Ty),d(x,Ty),d(y,Tx), |d(x,Tx)−d(y,Ty)| and |d(x,Ty)−d(y,Tx)|. The asymptotic regularity of the self-mapping T on X and the convergence of Cauchy sequences to a unique fixed point are also discussed if (X,d) is complete. Subsequently, (T, S) generalized cyclic p-contraction pairs are discussed on a pair of non-empty, in general, disjoint subsets of X. The proposed contraction involves a combination of several distances associated with the (T, S)-pair. Some properties demonstrated are: (a) the asymptotic convergence of the relevant sequences to best proximity points of both sets is proved; (b) the best proximity points are unique if the involved subsets are closed and convex, the metric is norm induced, or the metric space is a uniformly convex Banach space. It can be pointed out that both metric and a metric-like (or dislocated metric) possess the symmetry property since their respective distance values for any given pair of elements of the corresponding space are identical after exchanging the roles of both elements.This research was funded by Basq ue Government, Grant number IT1555-22

On Some Properties of a Class of Eventually Locally Mixed Cyclic/Acyclic Multivalued Self-Mappings with Application Examples

In this paper, a multivalued self-mapping is defined on the union of a finite number of subsets p(≥2) of a metric space which is, in general, of a mixed cyclic and acyclic nature in the sense that it can perform some iterations within each of the subsets before executing a switching action to its right adjacent one when generating orbits. The self-mapping can have combinations of locally contractive, non-contractive/non-expansive and locally expansive properties for some of the switching between different pairs of adjacent subsets. The properties of the asymptotic boundedness of the distances associated with the elements of the orbits are achieved under certain conditions of the global dominance of the contractivity of groups of consecutive iterations of the self-mapping, with each of those groups being of non-necessarily fixed size. If the metric space is a uniformly convex Banach one and the subsets are closed and convex, then some particular results on the convergence of the sequences of iterates to the best proximity points of the adjacent subsets are obtained in the absence of eventual local expansivity for switches between all the pairs of adjacent subsets. An application of the stabilization of a discrete dynamic system subject to impulsive effects in its dynamics due to finite discontinuity jumps in its state is also discussed.Basque Government, Grant IT1555-22