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Generalized ( ψ , α , β )—Weak Contractions for Initial Value Problems

Author

Listed:
  • Piyachat Borisut

    (KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Poom Kumam

    (KMUTT-Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
    KMUTT-Fixed Point Theory and Applications Research Group, Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand)

  • Vishal Gupta

    (Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana 133207, Haryana, India)

  • Naveen Mani

    (Department of Mathematics, Maharishi Markandeshwar (Deemed to be University), Mullana 133207, Haryana, India)

Abstract

A class of generalized ( ψ , α , β ) —weak contraction is introduced and some fixed-point theorems in a framework of partially ordered metric spaces are proved. The main result of this paper is applied to a first-order ordinary differential equation to find its solution.

Suggested Citation

  • Piyachat Borisut & Poom Kumam & Vishal Gupta & Naveen Mani, 2019. "Generalized ( ψ , α , β )—Weak Contractions for Initial Value Problems," Mathematics, MDPI, vol. 7(3), pages 1-14, March.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:3:p:266-:d:214227
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    References listed on IDEAS

    as
    1. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
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    Cited by:

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    2. Sahar Mohamed Ali Abou Bakr, 2021. "Cyclic G‐Ω‐Weak Contraction‐Weak Nonexpansive Mappings and Some Fixed Point Theorems in Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2021(1).

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