Open Access Research

Common fixed points and best approximations in locally convex spaces

Saleh Abdullah Al-Mezel

Author Affiliations

Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Fixed Point Theory and Applications 2011, 2011:99  doi:10.1186/1687-1812-2011-99

Published: 7 December 2011

Abstract

We extend the main results of Aamri and El Moutawakil and Pant to the weakly compatible or R-weakly commuting pair (T, f) of maps, where T is multivalued. As applications, common fixed point theorems are obtained for new class of maps called R-subcommuting maps in the setup of locally convex topological vector spaces. We also study some results on best approximation via common fixed point theorems.

2000 MSC 41A65; 46A03; 47H10; 54H25.

Keywords:
best approximations; common fixed points; locally convex spaces; R-subcommuting maps; R-weakly commuting.