Multivalued Contractions Research Articles

New Fixed Point Results via a Graph Structure

The main aim of this paper is to introduce and study some fixed point results for rational multivalued G-contraction and F-Khan-type multivalued contraction mappings on a metric space with a graph. At the end, we give an illustrative example.

Fixed-Point Study of Generalized Rational Type Multivalued Contractive Mappings on Metric Spaces with a Graph

The main result of this paper is a fixed-point theorem for multivalued contractions obtained through an inequality with rational terms. The contraction is an F-type contraction. The results are obtained in a metric space endowed with a graph. The main theorem is supported by illustrative examples. Several results as special cases are obtained by specific choices of the control functions involved in the inequality. The study is broadly in the domain of setvalued analysis. The methodology of the paper is a blending of both graph theoretic and analytic methods.

Existence for Impulsive Semilinear Functional Differential Inclusions

In this paper we investigate the existence of solutions for first-order impulsive semilinear functional differential inclusions in Banach spaces. Sufficient condition for the existence is obtained with the well-known Covitz and Nadler’s fixed point theorem for multivalued contractions.

Multivalued problems via orthogonal contraction mappings with application to fractional differential equation

In this manuscript, we give a partial answer to Reich’s problem on multivalued contraction mappings and generalize Mizoguchi–Takahashi’s fixed point theorem using a new approach of multivalued orthogonal $$(\tau ,F)$$ -contraction mappings in the framework of orthogonal metric spaces. We give a nontrivial example to prove the validity of our results. Some interesting consequences are also deduced. Finally, as application, we prove the existence and uniqueness of the solution of a nonlinear fractional differential equation.

Solutions of Fractional Differential Type Equations by Fixed Point Techniques for Multivalued Contractions

This paper involves extended b − metric versions of a fractional differential equation, a system of fractional differential equations and two-dimensional (2D) linear Fredholm integral equations. By various given hypotheses, exciting results are established in the setting of an extended b − metric space. Thereafter, by making consequent use of the fixed point technique, short and simple proofs are obtained for solutions of a fractional differential equation, a system of fractional differential equations and a two-dimensional linear Fredholm integral equation.

Fixed points and sets of multivalued contractions: an advanced survey with some new results

The existence of fixed points and, in particular, coupled fixed points is investigated for multivalued contractions in complete metric spaces. Multivalued coupled fractals are furthermore explored as coupled fixed points of certain induced operators in hyperspaces, i.e. as coupled compact subsets of the original spaces. The structure of fixed point sets is considered in terms of absolute retracts. We also formulate a continuation principle for multivalued contractions as a nonlinear alternative based on the topological essentiality. Two illustrative examples about coupled multivalued fractals are supplied.

Ciric type multi-valued $alpha _{ast }$-$eta _{ast }$-$theta $-contractions on b-metric spaces with applications

‎In this paper‎, ‎we give sufficient conditions for the existence of solutions‎ of a system of Volterra-type integral inclusion equations using new sort of‎ multi-valued contractions‎, ‎named as generalized multi-valued $alpha _{ast‎} ‎$-$eta _{ast }$-$theta $-contractions defined on $alpha $-complete‎ ‎b-metric spaces‎. ‎We give its relevance to fixed point results‎. ‎We set up an‎ ‎example to elucidate our main results‎.

Fixed point of multivalued contractions by altering distances with application to nonconvex Hammerstein type integral inclusions

Fixed point of multivalued contractions by altering distances with application to nonconvex Hammerstein type integral inclusions

Some best proximity point results for multivalued mappings on partial metric spaces

In this paper, we introduce two new concepts of Feng-Liu type multivalued contraction mapping and cyclic Feng-Liu type multivalued contraction mapping. Then, we obtain some new best proximity point results for such mappings on partial metric spaces by considering Feng-Liu's technique. Finally, we provide examples to show the effectiveness of our results.

Best proximity point theorems for proximal multi-valued contractions

In this paper, we introduce new classes of proximal multi-valued contractions in a metric space and proximal multi-valued nonexpansive mappings in a Banach space and show the existence of best proximity points for both classes. Further, for proximal multi-valued nonexpansive mappings, we prove a best proximity point theorem on starshape sets. As a consequence, we also obtain some new fixed point theorems. Finally, we give some examples to illustrate our main results.

Existence results for a nonlinear fractional differential inclusion

In this paper, we establish some existence results for higher-order nonlinear fractional differential inclusions with multi-strip conditions, when the right-hand side is convex-compact as well as nonconvexcompact values. First, we use the nonlinear alternative of Leray-Schauder type for multivalued maps. We investigate the next result by using the well-known Covitz and Nadler?s fixed point theorem for multivalued contractions. The results are illustrated by two examples.

Common Fixed Point Results for Set-valued Integral Type Contractions on Metric Spaces with Directed Graph

The aim of this paper is to establish new common fixed pointresults for multivalued integral type contraction mappings on a family of sets endowed with a graph. The obtained results generalize several recent ones. An example of application is included to illustrate the main existence theorem.

Some New Extensions of Multivalued Contractions in a b-metric Space and Its Applications

The Hβ-Hausdorff–Pompeiu b-metric for β∈[0,1] is introduced as a new variant of the Hausdorff–Pompeiu b-metric H. Various types of multi-valued Hβ-contractions are introduced and fixed point theorems are proved for such contractions in a b-metric space. The multi-valued Nadler contraction, Czervik contraction, q-quasi contraction, Hardy Rogers contraction, weak quasi contraction and Ciric contraction existing in literature are all one or the other type of multi-valued Hβ-contraction but the converse is not necessarily true. Proper examples are given in support of our claim. As applications of our results, we have proved the existence of a unique multi-valued fractal of an iterated multifunction system defined on a b-metric space and an existence theorem of Filippov type for an integral inclusion problem by introducing a generalized norm on the space of selections of the multifunction.

Multivalued weak cyclic \u03b4-contraction mappings

In this paper, we propose some new type of weak cyclic multivalued contraction mappings by generalizing the cyclic contraction using the δ-distance function. Several novel fixed point results are deduced for such class of weak cyclic multivalued mappings in the framework of metric spaces. Also, we construct some examples to validate the usability of the results. Various existing results of the literature are generalized.

Neutral multivalued integro-differential evolution equations with infinite state-dependent delay

Our problem through this work is to give the existence of mild solutions for the first order class of neutral functional multivalued integro-differential evolution equations with infinite state-dependent delay using the nonlinear alternative of Frigon for multivalued contraction maps in Fréchet spaces combined with the semi-group theory.

Higher Order of Convergence with Multivalued Contraction Mappings

In this paper, we establish some theorems of fixed point on multivalued mappings satisfying contraction mapping by using gauge function. Furthermore, we use Q - and R -order of convergence. Our main results extend many previous existing results in the literature. Consequently, to substantiate the validity of proposed method, we give its application in integral inclusion.

Global Optimization and Common Best Proximity Points for Some Multivalued Contractive Pairs of Mappings

In this paper, we study a problem of global optimization using common best proximity point of a pair of multivalued mappings. First, we introduce a multivalued Banach-type contractive pair of mappings and establish criteria for the existence of their common best proximity point. Next, we put forward the concept of multivalued Kannan-type contractive pair and also the concept of weak Δ-property to determine the existence of common best proximity point for such a pair of maps.

FIXED POINT THEOREMS FOR SUBSEQUENTIALLY MULTI-VALUED F_\delta -CONTRACTIONS IN METRIC SPACES

The aim of this paper is to prove common fixed point theorems for multivalued contraction of Wordowski type, by using the concept of subsequential continuity in the setting of set valued context contractions with compatibility. We have also given an example and an application to integral inclusions of Fredholm type to support our results.

Fixed Points for Multivalued Weighted Mean Contractions in a Symmetric Generalized Metric Space

This paper defines two new concepts: the concept of multivalued left-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space and the concept of multivalued right-weighted mean contractions in the generalized sense of Nadler in a symmetric generalized metric space, and demonstrates fixed-point theorems for them. For these, we demonstrated two fixed-point existence theorems and their corollaries, by using the properties of the regular-global-inf function and the properties of symmetric generalized metric spaces, respectively. Moreover, we demonstrated that the theorems can be applied in particular cases of inclusion systems. This article contains not only an example of application in science, but also an example of application in real life, in biology, in order to find an equilibrium solution to a prey–predator-type problem. The results of this paper extend theorems for multivalued left-weighted mean contractions in the generalized sense of Nadler, demonstrating that some of the results given by Rus (2008), Mureșan (2002), and Nadler (1969) in metric spaces can also be proved in symmetric generalized metric spaces.

Multivalued weakly Picard operators via simulation functions with application to functional equations

<abstract> <p>The aim of this paper is to introduce the notion of Suzuki type multivalued contraction with simulation functions and then to set up some new fixed point and data dependence results for these type of contraction mappings. We produce an example to support our results. Moreover, we present an application to functional equation arising in dynamical system.</p> </abstract>