Fixed point theorems for random pseudo-contractive mappings

Very recently in Fierro et al. (2009) [6], we obtained a general principle to prove the existence of Random Fixed Point Theorems. As a consequence of this, we have been able to obtain various generalizations for pseudo-contractive mappings with rather simple proofs. In addition, while we were deriving these extensions for random operators, some deterministic results arose, which also appear to be new.     

Chebyshev centers and fixed point theorems

Brodskii and Milman proved that there is a point in C(K)$C(K)$, the set of all Chebyshev centers of K, which is fixed by every surjective isometry from K into K whenever K   is a nonempty weakly compact convex subset having normal structure in a Banach space. Motivated by this result, Lim et al. raised the following question namely “does there exist a point in C(K)$C(K)$ which is fixed by every isometry from K into K?”. In fact, Lim et al. proved that “if K is a nonempty weakly compact convex subset of a uniformly convex Banach space, then the Chebyshev center of K is fixed by every isometry T from K into K”. In this paper, we prove that if K   is a nonempty weakly compact convex set having normal structure in a strictly convex Banach space and F$\mathfrak{F}$ is a commuting family of isometry mappings on K   then there exists a point in C(K)$C(K)$ which is fixed by every mapping in F$\mathfrak{F}$.     

Fixed points of commuting holomorphic mappings other than the Wolff point

Let be the unit disc of and let be such that . For 1$">, let . We study the behavior of on . In particular, we prove that . As a consequence, besides conditions for , we prove a conjecture of C. Cowen in case and are univalent mappings.

     

Fixed point of multivalued mapping in uniform spaces

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.     

Fixed point theorems for fuzzy mappings

This paper presents some new fixed point theorems for fuzzy mappings. The results given in this paper improve and extend some recent results.     

KKM-type theorems for best proximity points

Let us consider two nonempty subsets A,B of a normed linear space X, and let us denote by 2^B the set of all subsets of B. We introduce a new class of multivalued mappings {T:A→2^B}, called R-KKM mappings, which extends the notion of KKM mappings. First, we discuss some sufficient conditions for which the set ∩{T(x):x∈A} is nonempty. Using this nonempty intersection theorem, we attempt to prove a extended version of the Fan-Browder multivalued fixed point theorem, in a normed linear space setting, by providing an existence of a best proximity point.     

Convergence of sequences of fuzzy numbers and fixed point theorems for increasing fuzzy mappings and application

In this paper, we discuss some properties of the convergence of sequences of fuzzy numbers and obtain some fixed point theorems for increasing fuzzy mappings. And as applications, we give two examples. One is about fishery production, which discusses the balance problems between the quantity of catching fish and the increase in the quantity of fish that is produced by the reproduction and growth of fish. Another is about the solvability of the equation of fuzzy numbers.     

Fixed point theorems for generalized weakly S-contractive mappings in partial metric spaces

In this paper, we establish some unique xed point theorems for generalized weakly S-contractive with nondecreasing and weakly increasing mappings in complete partial metric space. Also, we give some examples for strengthens of our main results.     

Fixed point theorems under the interior condition

We show a fixed point theorem for condensing mappings under a new condition of the Leray-Schauder type. We call it the Interior Condition. We also discuss examples that demonstrate the independence of these two conditions.

     

Fixed point theorems and convergence theorems for some generalized nonexpansive mappings

We introduce some condition on mappings. The condition is weaker than nonexpansiveness and stronger than quasinonexpansiveness. We present fixed point theorems and convergence theorems for mappings satisfying the condition.     

Fixed point theorems for multivalued operators and application to discontinuous quasilinear BVP's

In this article, we prove an abstract fixed point theorem for increasing multivalued operators in ordered topological spaces, which provides an efficient tool to obtain qualitative results on the solution set of discontinuous quasilinear elliptic boundary value problems. In particular, we are able to show the existence of extremal solutions of such problems.     

Fixed point theorems for multifunctions with applications to discontinuous operator and differential equations

In this paper we study existence of minimal and maximal fixed points for increasing multivalued functions in ordered topological vector spaces, and apply the obtained results to operator equations and quasilinear elliptic boundary value problems involving discontinuous nonlinearities.     

Fixed points of asymptotic contractions

Let be a contractive gauge function in the sense that φ is continuous, φ(s)<s for s>0, and if f:M→M satisfies d(f(x),f(y))?φ(d(x,y)) for all x,y in a complete metric space (M,d), then f always has a unique fixed point. It is proved that if T:M→M satisfies

     

Fixed point theorems for some generalized multivalued nonexpansive mappings

In this paper, we introduce a condition on multivalued mappings which is a multivalued version of condition (C_λ) defined by Garcia-Falset et al. (2011) [3]. It is shown here that some of the classical fixed point theorems for multivalued nonexpansive mappings can be extended to mappings satisfying this condition. Our results generalize the results in Lim (1974), Lami Dozo (1973), Kirk and Massa (1990), Garcia-Falset et al. (2011), Dhompongsa et al. (2009) and Abkar and Eslamian (2010) [4], [5], [6], [3], [7] and [8] and many others.     

Fixed point theorems in ordered abstract spaces

We extend some fixed point theorems in -spaces, obtaining extensions of the Banach fixed point theorem to partially ordered sets.

     

Fixed point theorems in fuzzy metric spaces

In this paper, we state and prove some common fixed point theorems in fuzzy metric spaces. These theorems generalize and improve known results (see [1]).     

Fixed point and selection theorems in hyperconvex spaces

It is shown that a set-valued mapping of a hyperconvex metric space which takes values in the space of nonempty externally hyperconvex subsets of always has a lipschitzian single valued selection which satisfies for all . (Here denotes the usual Hausdorff distance.) This fact is used to show that the space of all bounded -lipschitzian self-mappings of is itself hyperconvex. Several related results are also obtained.

     

Fixed point theorems in metric spaces

In this paper, we establish two general theorems for equivalence between the Meir–Keeler type contractive conditions and the contractive definitions involving gauge functions. One of these theorems is an extension of a recent result of Lim (On characterization of Meir–Keeler contractive maps, Nonlinear Anal. 46 (2001) 113–120).