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Common coupled fixed point theorems for \(w^*\)-compatible mappings without mixed monotone property

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Abstract

In this paper, we show that the mixed \(g\)-monotone property in coupled coincidence point theorems can be replaced by generalized property. Hence, these results can be applied in a much wider class of problems. We also study the condition for the uniqueness of a common coupled fixed point and give some example of nonlinear contraction mappings where the existence of the common coupled fixed point cannot be obtained by the mixed monotone property, but it follows by our results. At the end of this paper, we give an open problems for further investigation.

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Acknowledgments

The first author would like to thank the Research Professional Development Project under the Science Achievement Scholarship of Thailand (SAST) and the second author this work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS-UEFISCDI, project number PN-II-ID-PCE-2011-3-0094. The third author this work was supported by the Commission on Higher Education, the Thailand Research Fund and the King Mongkut’s University of Technology Thonburi (KMUTT) (Grant No. MRG5580213).

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, 10140, Thailand

    Wutiphol Sintunavarat & Poom Kumam

  2. Department of Mathematics, Babeş-Bolyai University Cluj-Napoca, Kogalniceanu 1, 400084, Cluj-Napoca, Romania

    Adrian Petruşel

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  1. Wutiphol Sintunavarat
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  2. Adrian Petruşel
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  3. Poom Kumam
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Correspondence to Poom Kumam.

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Sintunavarat, W., Petruşel, A. & Kumam, P. Common coupled fixed point theorems for \(w^*\)-compatible mappings without mixed monotone property. Rend. Circ. Mat. Palermo 61, 361–383 (2012). https://doi.org/10.1007/s12215-012-0096-0

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  • DOI: https://doi.org/10.1007/s12215-012-0096-0

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