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A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications

Author

Listed:
  • Dilip Jain

    (Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007 Gujarat, India)

  • Anantachai Padcharoen

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand)

  • Poom Kumam

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru, Bangkok 10140, Thailand)

  • Dhananjay Gopal

    (Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat-395007 Gujarat, India)

Abstract

The purpose of this paper is to present a new approach to study the existence of fixed points for multivalued F -contraction in the setting of modular metric spaces. In establishing this connection, we introduce the notion of multivalued F -contraction and prove corresponding fixed point theorems in complete modular metric space with some specific assumption on the modular. Then we apply our results to establish the existence of solutions for a certain type of non-linear integral equations.

Suggested Citation

  • Dilip Jain & Anantachai Padcharoen & Poom Kumam & Dhananjay Gopal, 2016. "A New Approach to Study Fixed Point of Multivalued Mappings in Modular Metric Spaces and Applications," Mathematics, MDPI, vol. 4(3), pages 1-9, August.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:3:p:51-:d:75531
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    References listed on IDEAS

    as
    1. Parin Chaipunya & Chirasak Mongkolkeha & Wutiphol Sintunavarat & Poom Kumam, 2012. "Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-14, April.
    2. Parin Chaipunya & Chirasak Mongkolkeha & Wutiphol Sintunavarat & Poom Kumam, 2012. "Erratum to “Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces”," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-2, July.
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