Point Theorems For Multivalued Mappings Research Articles

Some fixed point theorems for multi-valued mappings on reflexive Banach spaces

Some fixed point theorems for multi-valued mappings on reflexive Banach spaces

Common stationary points of multivalued mappings on bounded metric spaces

Necessary and sufficient conditions for the existence of common stationary points of two multivalued mappings and common stationary point theorems for multivalued mappings on bounded metric spaces are given. Our results extend the theorems due to Fisher in 1979, 1980, and 1983 and Ohta and Nikaido in 1994.

Some results on coincidence points

In this paper we prove some coincidence point theorems for nonself single-valued and multivalued maps satisfying a nonexpansive condition. These extend fixed point theorems for multivalued maps of a number of authors.

Fixed point theorems for multivalued mappings in probabilistic metric spaces

In this paper we prove a fixed point theorem for multivalued mappings in probabilistic metric spaces. Some applications in fuzzy metric and random normed spaces are given.

Maximal elements and fixed points for binary relations on topological ordered spaces

Topological semilattices are partially ordered topological spaces X in which each pair of elements x, x′ ∈ X has a least upper bound x V x′ and the function ( x, x′)↦ x V x′ is continuous. We establish in such a context an order theoretical version of the classical result of Knaster-Kuratowski-Mazurkiewicz, as well as fixed point theorems for multivalued mappings. One can then, as in the context of topological vector spaces, obtain existence results for the largest elements of a weak preference relation or maximal elements for a strict preference relation. Beyond these particular results, we wish to attract attention to path-connected topological semilattices, examples of which will be found in the introduction, and their rich geometric structure — a geometric structure rich enough to provide order theoretical versions of some of the basic tools from mathematical economics and, therefore, also an alternative to the usual convexity assumptions.

On random approximations and a random fixed point theorem for multivalued mappings defined on unbounded sets in hilbert spaces

A random approximation theorem for multivalued nonexpansive random operator defined on an unbounded subset of a Hilbert spaces is proved. As an application of our theorem, a random fixed point theorem is derived

Fixed Point Theorems for Multi-Valued Mappings in Subsymmetrizable Spaces

Fixed Point Theorems for Multi-Valued Mappings in Subsymmetrizable Spaces

Fixed point theorems for multi-valued mappings in subsymmetrizable spaces

Three fixed point theorems for multi-valued mappings in symmetric spaces with closure operator are proved. As corollaries of these theorems we obtain the existence of fixed points of mappings in compact metric spaces. Another corollary of the last theorem extends a condition of Kannan’s theorem.

Section Theorems on H-Spaces with Applications

Some further generalizations of Fan′s and Shih-Tan′s geometric theorems for convex sets are obtained. As applications, in Sections 3-5, we utilize these results to study the minimax inequalities, and the fixed point theorems for multi-valued mappings. The results presented in this paper generalize the von Neumann and the Fan-Kneser minimax theorems and some others recent results.

Some Fixed Point Theorems for Multivalued Maps and Applications

In order to obtain some existence results for certain generalized eigenvalue problems nd to study certain parametrized boundary value problems for second order differential nclusions, we generalize some fixed point theorems for completely continuous (single-valued) aps to the multivalued case. We illustrate our results with some examples.

Coincidence point theorems for multivalued mappings

Some new coincidence point and fixed point theorems for multivalued mappings in complete metric space are proved. The results presented in this paper enrich and extend the corresponding results in [5-16, 20-25, 29].

Fixed point theorems for multivalued mappings in Banach spaces

Fixed point theorems for multivalued mappings in Banach spaces

Fixed point theorems for multivalued mappings in some classes of fuzzy metric spaces

Using the probabilistic function of noncompactness a fixed point theorem for multivalued mappings in probabilistic metric spaces is proved. As an application a fixed point theorem for multivalued mappings in fuzzy metric spaces is obtained.

Some fixed point theorems for multivalued mappings

Some fixed point theorems for multivalued mappings

Some properties of measures of noncompactness in paranormed spaces

This paper presents new properties of important measures of noncompactness in paranormed spaces. Using these properties some fixed point theorems for multivalued mappings in general topological vector spaces are obtained in a straightforward way.

Coincidence and fixed points of nonlinear Hybrid contractions

In this Der, we show the existence of solutions of functional equations fx ∈ sx∩tx and x=fx ∈ sx∩Tx under certain contraction and asymptotic regularity conditions, where f, S and T are single‐valued and multl‐valued mappings on a metric space, respectively. We also observe that MukherJee′s fixed point theorem for a single‐valued mapping commuting with a multl‐valued mapping admits of a counterexample and suggest some modifications. While doing so, we also answer an open question raised in [I] and [2]. Moreover, our results extend and unify a multitude of fixed point theorems for multi‐valued mappings.

Fixed point theorems for multivalued mappings

Fixed point theorems for multivalued mappings

Some applications of fixed point theorems for multivalued mappings on minimax problems in topological vector spaces

Using some fixed point theorems for multivalued mappings in topological .vector space, which is not necessarily locally convex, in this paper some generalizations of Theorem 13 [1], Theorem 15 [1] and Theorem 4 [16] are proved.

Pure strategy Nash equilibrium points and the Lefschetz fixed point theorem

A pure strategy Nash equilibrium point existence theorem is established for a class ofn-person games with possibly nonacyclic (e.g. disconnected) strategy sets. The principal tool used in the proof is a Lefschetz fixed point theorem for multivalued maps, due to Eilenberg and Montgomery, which extends their better known. Eilenberg-Montgomery fixed point theorem (EMT) [Eilenberg/Montgomery, Theorem 1, p. 215] to nonacyclic spaces. Special cases of the existence theorem are also discussed.

Nonzero solutions of nonlinear systems of differential equations via fixed point theorems for multivalued maps

IN THE present paper we consider a nonlinear System of differential equations (.) x’ = A(t, x)x + F(t, x) and a condition (. .) x E B, x(t) $ 0. where A(t, x) is a n x n real matrix defined and continuous on A x R” (A denotes a compact interval of R), F : A x R” + R” is continuous and B is a Banach space of continuous functions. To solve this problem, we use a comparison technique and we reduce the existence of solutions for this problem to that of a fixed point of a suitably defined multivalued map S (see also Anichini [l], Kartsatos [3] and Schmitt [4]). In these papers the Eilenberg-Montgomery futed point theorem is applied. First we consider the problem (. . .) x’ = A(& x)x and the condition (..). Using the Eilenberg-Montgomery Theorem 3.1 of [3]. fixed point theorem, we improve