Multivalued fi�xed point theorems without strong compactness via a generalization of midpoint convexity (original) (raw)

New common fixed point theorems for multivalued maps

Applied General Topology, 2014

Common fixed point theorems for a new class of multivalued maps are obtained, which generalize and extend classical fixed point theorems of Nadler and Reich and some recent Suzuki type fixed point theorems.

Common fixed point theorems for multivalued mappings

Pacific Journal of Mathematics, 1981

Some results on common fixed points for a pair of multivalued mappings defined on a closed subset of a complete metric space are obtained. Our work extends some of the known results due to Itoh; Isέki; and Rus.

A Common Fixed Point Theorem for a Pair of Nonself Multi-valued Mappings

2012

A common fixed point theorem for a pair of nonself multi-valued mappings in complete metrically convex metric spaces is proved which generalizes some earlier known results due to Khan et al. [9], Bianchini [2], Chatterjea [3], Khan et al. [10] and others. An illustrative example is also discussed.

A fixed point theorem without convexity

2000

The purpose of this paper is to extend Himmelberg's fixed point theorem replacing the usual convexity in topological vector spaces by an abstract topological notion of convexity which generalizes classical convexity as well as several metric convexity structures found in the literature.

Abstract Convexity and Fixed Points

Journal of Mathematical Analysis and Applications, 1998

The purpose of this paper is to extend Himmelberg's fixed-point theorem, replacing the usual convexity in topological vector spaces with an abstract topological notion of convexity that generalizes classical convexity as well as several metric convexity structures found in the literature. We prove the existence, under weak hypotheses, of a fixed point for a compact approachable map, and we provide sufficient conditions under which this result applies to maps whose values are convex in the abstract sense mentioned above.

Fixed point theorems for single-valued and multi-valued maps

Nonlinear Analysis: Theory, Methods & Applications, 2011

a b s t r a c t Coincidence and fixed point theorems for single-valued and multi-valued maps generalizing recent results of Suzuki and Kikkawa are obtained. Various applications, including the existence of common solutions of certain functional equations are presented.

Common fixed point theorems for multi-valued maps

Acta Mathematica Scientia, 2012

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.

Fixed-Point Theorems for Multivalued Non-Expansive Mappings Without Uniform Convexity

Abstract and Applied …, 2003

Let X be a Banach space whose characteristic of noncompact convexity is less than 1 and satisfies the nonstrict Opial condition. Let C be a bounded closed convex subset of X, KC(C) the family of all compact convex subsets of C, and T a nonexpansive mapping from C into KC(C). We prove that T has a fixed point. The nonstrict Opial condition can be removed if, in addition, T is a 1-χcontractive mapping.