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Two coupled weak contraction theorems in partially ordered metric spaces

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Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas Aims and scope Submit manuscript

Abstract

In this work we establish two general weak coupled contraction mapping theorems in partially ordered metric spaces. Weak contractions are extensions of contractive mappings which are intermediate to Banach’s contractions and nonexpansive mappings. They have been considered elaborately in recent literatures. Our works generalise the coupled contraction mapping theorem established by Gnana Bhaskar and Lakshmikantham (Nonlinear Anal. TMA, 65:1379–1393, 2006) to weak coupled contractions. We have used certain control functions in our theorems. Two illustrative examples are given.

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Acknowledgments

The work is partially supported by Council of Scientific and Industrial Research, India (No. 25(0168)/09/EMR-II). The first author gratefully acknowledges the support.

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Authors and Affiliations

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

    Binayak S. Choudhury

  2. Department of Mathematics, Siliguri Institute of Technology, P.O.-Sukna, Darjeeling, 734009, West Bengal, India

    Amaresh Kundu

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  1. Binayak S. Choudhury
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  2. Amaresh Kundu
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Correspondence to Amaresh Kundu.

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Choudhury, B.S., Kundu, A. Two coupled weak contraction theorems in partially ordered metric spaces. RACSAM 108, 335–351 (2014). https://doi.org/10.1007/s13398-012-0095-1

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