## Multi-valued contraction mappings

In § 3 the two fixed point theorems for multi-valued contraction map- pings are proved. The first, a generalization of the contraction mapping principle of Banach,

Oct 15, 2009 Two concepts of nonlinear contractions for multi-valued mappings in complete metric spaces are introduced and three fixed point theorems are  states that a contraction mapping of a complete metric space X into itself has a unique fixed point. A similar theorem for multivalued contraction mappings has  In this paper, the famous Banach contraction principle and Caristi's fixed point theorem are generalized to the case of multi-valued mappings. Our results are  Dec 22, 2014 The purpose of this paper is to study the existence of fixed points for contractive- type multivalued maps in the setting of modular metric spaces. Key words: Fixed point, multivalued contraction, generalized multivalued θ- complete metric space and T : X → X is a contraction mapping, i.e. d(Tx,Ty) ≤ Ld( x

## Two concepts of nonlinear contractions for multi-valued mappings in complete metric spaces are introduced and three fixed point theorems are proved.

Several extensions of these results have appeared in literature. On the other hand, Banach's contraction principle is extended to multi- valued mappings by Nadler  Most recently, the author  extended Nadler's mutlivalued fixed point theorem to the case of monotone multivalued mappings in metric spaces endowed with a  of multi-valued contraction mappings and established that a multi-valued contraction mapping possesses a fixed point in a complete metric space. Subsequently  Multi-valued quasi-contractions are also discussed.  V. W. Bryant, A remark on a fixed-point theorem for iterated mappings, Amer. Math. Monthly 75 (1968)

### A map T:X → X is called contraction if there exists 0 ≤ ˜ < 1 such that d(Tx,Ty) ≤ ˜d(x,y), for all x,y ∈ X. T:X → 2Y. Abstract In this paper, we prove a fixed point theorem and a common fixed point theorem for multi valued mappings in complete b-metric spaces. Keywords: b-Metric space, Multi-valued mappings, Contraction , Fixed

THE POWER INDICES FOR MULTI-CHOICE MULTI-VALUED GAMES Hsiao, Chih-Ru, Taiwanese Journal of Mathematics, 2004 Common Fixed Points for Multivalued Mappings in Complex Valued Metric Spaces with Applications Ahmad, Jamshaid, Klin-Eam, Chakkrid, and Azam, Akbar, Abstract and Applied Analysis, 2013 Multi-valued nonlinear contraction mappings. Abstract. Two concepts of nonlinear contractions for multi-valued mappings in complete metric spaces are introduced and three fixed point theorems are proved. Presented theorems are generalizations of very recent fixed point theorems due to Klim and Wardowski [D.

### He extended the Banach contraction principle to multi-valued mappings. Many authors have studied the existence and uniqueness of fixed points for a multi-

Dec 22, 2014 The purpose of this paper is to study the existence of fixed points for contractive- type multivalued maps in the setting of modular metric spaces. Key words: Fixed point, multivalued contraction, generalized multivalued θ- complete metric space and T : X → X is a contraction mapping, i.e. d(Tx,Ty) ≤ Ld( x  He extended the Banach contraction principle to multi-valued mappings. Many authors have studied the existence and uniqueness of fixed points for a multi-  Several extensions of these results have appeared in literature. On the other hand, Banach's contraction principle is extended to multi- valued mappings by Nadler  Most recently, the author  extended Nadler's mutlivalued fixed point theorem to the case of monotone multivalued mappings in metric spaces endowed with a  of multi-valued contraction mappings and established that a multi-valued contraction mapping possesses a fixed point in a complete metric space. Subsequently

## In § 3 the two fixed point theorems for multi-valued contraction map- pings are proved. The first, a generalization of the contraction mapping principle of Banach,

A mapping will be called a quasi-contraction iff for some and all . In the present paper the mappings of this kind are investigated. The results presented here show that the condition of quasi-contractivity implies all conclusions of Banach's contraction principle. Multi-valued quasi-contractions are also discussed. In this paper, we introduce the concepts of graph-preserving multi-valued mapping and a new type of multi-valued weak G-contraction on a metric space endowed with a directed graph G. We prove some coincidence point theorems for this type of multi-valued mapping and a surjective mapping under some conditions. In this paper, we introduce generalized Wardowski type quasi-contractions called α - ( φ , Ω ) -contractions for a pair of multi-valued mappings and prove the existence of the common fixed point for such mappings. An illustrative example and an application are given to show the usability of our results. In this paper we investigate some fixed point results of Feng and Liu type multi-valued mappings in modular metric spaces. We also give an example to show that these results are more general versions of Feng and Liu’s theorem. In mathematics, a multivalued function is similar to a function, but may associate several values to each input.More precisely, a multivalued function from a domain X to a codomain Y associates to each x in X one or more values y in Y; it is thus a left-total binary relation. [citation needed] Some authors allow a multivalued function to have no value for some inputs (in this case a

of multi-valued contraction mappings and established that a multi-valued contraction mapping possesses a fixed point in a complete metric space. Subsequently  Multi-valued quasi-contractions are also discussed.  V. W. Bryant, A remark on a fixed-point theorem for iterated mappings, Amer. Math. Monthly 75 (1968)  Apr 10, 2018 for some classes of ℑ‐contraction mappings on Pompeiu‐Hausdorff multivalued type contraction mappings in dislocated b‐metric spaces  Abstract. We study the existence of fixed points for contraction multivalued mappings in modular metric spaces endowed with a graph. The notion of a  Feb 28, 2017 multi-valued contraction mappings. Let (X, d) be a complete metric space,. CB(X) be a collection of all nonempty closed and bounded subsets