We study property (T) and the fixed point property for actions on L p and other Banach spaces. We show that property (T) holds when L 2 is replaced by L p (and even a subspace/quotient of L p), and that in fact it is independent of 1 ≤ p < ∞. We show that the fixed point property for L p follows from property (T) when 1 < p < 2 + ε. For simple Lie groups and their lattices, we prove that the fi...

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

A. Rosenfeld [23] introduced the notion of a digitally continuous function between digital images, and showed that although digital images need not have fixed point properties analogous to those of the Euclidean spaces modeled by the images, there often are approximate fixed point properties of such images. In the current paper, we obtain additional results concerning fixed points and approxima...

If X is the dual space of a given Banach space E , X = E*, we say that X has the weak* fixed point property (w*-fpp) if for every nonempty weak* compact (that is, cr(X, E)-co~npact) convex subset C of X and every nonexpansive mapping T : C + C we have Fix(T) # 0. Which subsets of X are weak* compact depends on the choice of pre-dual. Thus, when discussing the w*-fpp it is important that we have...

Nonexpansive mappings have been studied extensively in recent years by many authors.The first fixed point theorem of a general nature for nonlinear nonexpansive mappings in noncompact setting were proved independently by Browder [8] and Gohde [12]. Later on, Kirk [17] proved the same results under slightly weaker assumptions. A fundamental problem in fixed point theory of nonexpansive mappings ...

Let K be a nonempty closed convex subset of a real Banach space E and T be a Lipschitz pseudocontractive self-map of K with F (T ) := {x ∈ K : Tx = x} 6= ∅. An iterative sequence {xn} is constructed for which ||xn − Txn|| → 0 as n → ∞. If, in addition, K is assumed to be bounded, this conclusion still holds without the requirement that F (T ) 6= ∅. Moreover, if, in addition, E has a uniformly G...

In this paper, we work with the notion of the measure of nonhyperconvexity introduced by Cianciaruso and De Pascale [6] in order to obtain new fixed-point theorems in hyperconvex metric spaces. This class of metric spaces was introduced by Aronszajn and Panitchpakdi [1] in 1956 to study problems on extension of uniformly continuous mappings. Several and interesting properties of these spaces we...

In this lecture, we discuss splitting algorithms for convex minimization problems with objective given by the sum of two nonsmooth functions. We start with the fixed point property of such problems and derive a general scheme of splitting algorithm based on fixed point iteration. This covers Douglas-Rachford splitting and Peaceman-Rachford splitting algorithms. We also discuss the convergence r...

The purpose of this paper is to obtain the common fixed point results for two pair of weakly compatible mapping by using common (CLR) property in partial metric space. Also we extend the very recent results which are presented in [17,  Muhammad Sarwar, Mian Bahadur Zada and Inci M. Erhan, Common Fixed Point Theorems of Integral type on Metric Spaces and application to system of functional equat...