Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings. (16th July 2012)

• Record Type: Journal Article
• Authors: Bisht, R. K.
• Other Names: Shahzad Naseer Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2012(2012)
• Publication Date: 2012-07-16
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2012/786814
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem.