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Generalized nonexpansive mappings in ordered metric spaces and their (common) fixed points with applications

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

Abstract

We introduce a generalized nonexpansive condition for a map in an ordered metric space and derive fixed point theorems for a nondecreasing mapping. Moreover, common fixed point results are obtained for a pair of mappings satisfying an appropriate nonexpansive condition. To illustrate our results, we give throughout the paper some examples. Applications of the obtained results to integral equations and first-order periodic boundary value problems are presented.

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Acknowledgments

The authors express their gratitude to the referees for careful reading of the manuscript and the remarks which undoubtedly help them to improve it. The second author is grateful to the Ministry of Education, Science and Technological Development of Serbia.

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Authors and Affiliations

  1. Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg Mandir Hasaud, Raipur, 492101, Chhattisgarh, India

    Hemant Kumar Nashine

  2. Faculty of Mathematics, University of Belgrade, Studentski trg 16, 11000 , Beograd, Serbia

    Zoran Kadelburg

Authors
  1. Hemant Kumar Nashine
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  2. Zoran Kadelburg
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Correspondence to Hemant Kumar Nashine.

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Nashine, H.K., Kadelburg, Z. Generalized nonexpansive mappings in ordered metric spaces and their (common) fixed points with applications. RACSAM 108, 633–651 (2014). https://doi.org/10.1007/s13398-013-0131-9

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  • DOI: https://doi.org/10.1007/s13398-013-0131-9

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Mathematics Subject Classification (2010)

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