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Weak contractions on chains in a generalized metric space with a partial order

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Abstract

Weak contraction mapping principle is a generalization of the Banach contraction mapping principle. Weakly contractive mappings are intermediate to contraction mappings and nonexpansive mappings. They have been studied in several contexts. Metric fixed point theory in partially ordered spaces have rapidly developed in recent times. In this paper we extend the concept of weak contraction to subset of a partially ordered generalized metric space which are chains by themselves. It is noted that this weak contraction is different from weak contraction on the whole space. We prove here that under certain assumptions the weakly contractive mapping on certain chains will have a fixed point. Two illustrative examples are given.

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Acknowledgments

The work is supported by the Council of Scientific and Industrial Research, Government of India, under Research Project No - 25(0168)/09/EMR-II. The support is gratefully acknowledged. The authors acknowledge the suggestions of the learned referees.

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Authors and Affiliations

  1. Department of Mathematics, Bengal Engineering and Science University, Shibpur, P.O. - B. Garden, Howrah,  711103, West Bengal, India

    Binayak S. Choudhury & Pranati Maity

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  1. Binayak S. Choudhury
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  2. Pranati Maity
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Correspondence to Pranati Maity.

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Choudhury, B.S., Maity, P. Weak contractions on chains in a generalized metric space with a partial order. Afr. Mat. 25, 745–756 (2014). https://doi.org/10.1007/s13370-013-0146-6

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  • DOI: https://doi.org/10.1007/s13370-013-0146-6

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