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Some fixed point theorems for G-nonexpansive mappings on ultrametric spaces and non-Archimedean normed spaces with a graph

Mamghaderi H., Masiha H. P.

Journal of Mathematics and Applications

2016

Vol. 39

81--90

A very interesting approach in the theory of fixed point is some general structures was recently given by Jachymski by using the context of metric spaces endowed with a graph. The purpose of this article is to present some new fixed point results for G-nonexpansive mappings defined on an ultrametric space and non-Archimedean normed space which are endowed with a graph. In particular, we investigate the relationship between weak connectivity graph and the existence of fixed point for these mappings.

Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems

Shehu Y., Oguguo O.

Journal of Applied Analysis

2012

Vol. 18, nr 1

69-95

In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element in the fixed points set of an infinite family of relatively quasi-nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. We give several applications of our results in a Banach space. Our results extend many known recent results in the literature.

Common fixed points of nonexpansive mappings with applications to best and best simultaneous approximation

Chandok S., Narang T.D.

Journal of Applied Analysis

2012

Vol. 18, nr 1

33-46

We prove some new results on the existence of common fixed points for nonexpansive and asymptotically nonexpansive mappings in the framework of convex metric spaces. We also obtain some results on common fixed points from the set of best and best simultaneous approximations as applications. The proved results generalize and extend some of the known results in the literature.

Implicit and explicit constructions of sunny nonexpansive retractions in Banach spaces

Aleyner A., Reich S.

Journal of Mathematics and Applications

2007

Vol. 29

5-16

Implicit and explicit processes for eonstructing the unique sunny nonexpansive retraction onto the common fixed point set of either a finite or infmite family of nonexpansive mappings in a Banach space are proposed and corresponding convergence theorems are established.

Coincidence points an best proximity pair results for R-subweakly commuting multimaps

O'Regan D., Shahzad N.

Demonstratio Mathematica

2006

Vol. 39, nr 4

845-854

Some coincidence point theorems for R-subweakly commuting mappings satisfying a general contractive condition are proved. As applications, some best proximity pair results are also obtained and several related results in the literature are extended to a new class of noncommuting mappings.