Common Fixed Points and Best Approximation

Fixed Points and Best Approximation in Menger Convex Metric Spaces

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 ...

Common fixed points and best approximants in nonconvex domain

The aim of the paper is to show the validity of results of Imdad [7] in a domain which is not necessarily starshaped and mappings are not necessarily linear. Our results also improve, extend and generalize various existing known results in the literature.

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Common fixed-point results in best approximation theory

A common fixed-point generalization of the results of Dotson, Tarafdar, and Taylor is obtained which in turn extends a recent theorem by Jungck and Seasa to locally convex spaces. As applications of our work, we improve and unify well-known results on fixed points and common fixed points of beat approximation. @ 2003 Elsevier Science Ltd. All rights reserved. Keywords--common fixed point, Best ...

Invariant Points of Best Approximation and Best Simultaneous Approximation

In this paper we generalize and extend BrosowskiMeinardus type results on invariant points from the set of best approximation to the set of best simultaneous approximation, which is not necessarily starshaped. As a consequence some results on best approximation are deduced. The proved results extend and generalize some of the results of R. N. Mukherjee and V. Verma [Publ. de l’Inst. Math. 49(19...