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Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings

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  • R. K. Bisht

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.

Suggested Citation

  • R. K. Bisht, 2012. "Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-12, July.
    • Handle: RePEc:hin:jijmms:786814
    DOI: 10.1155/2012/786814
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    References listed on IDEAS

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    1. S. L. Singh & S. N. Mishra, 2002. "Coincidences and fixed points of reciprocally continuous and compatible hybrid maps," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 30, pages 1-9, January.
    2. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
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