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F -Convex Contraction via Admissible Mapping and Related Fixed Point Theorems with an Application

Author

Listed:
  • Y. Mahendra Singh

    (Department of Humanities and Basic Sciences, Manipur Institute of Technology, Takyelpat 795004, India)

  • Mohammad Saeed Khan

    (Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Al-Khod Muscat 123, Oman; mohammad@squ.edu.om)

  • Shin Min Kang

    (Department of Mathematics and RINS, Gyeongsang National University, Jinju 52828, Korea
    Center for General Education, China Medical University, Taichung 40402, Taiwan)

Abstract

In this paper, we introduce F -convex contraction via admissible mapping in the sense of Wardowski [Fixed points of a new type of contractive mappings in complete metric spaces. Fixed Point Theory Appl., 94 (2012), 6 pages] which extends convex contraction mapping of type-2 of Istrǎţescu [Some fixed point theorems for convex contraction mappings and convex non-expansive mappings (I), Libertas Mathematica, 1(1981), 151–163] and establish a fixed point theorem in the setting of metric space. Our result extends and generalizes some other similar results in the literature. As an application of our main result, we establish an existence theorem for the non-linear Fredholm integral equation and give a numerical example to validate the application of our obtained result.

Suggested Citation

  • Y. Mahendra Singh & Mohammad Saeed Khan & Shin Min Kang, 2018. "F -Convex Contraction via Admissible Mapping and Related Fixed Point Theorems with an Application," Mathematics, MDPI, vol. 6(6), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:6:p:105-:d:153399
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    Cited by:

    1. Gunasekaran Nallaselli & Arul Joseph Gnanaprakasam & Gunaseelan Mani & Zoran D. Mitrović & Ahmad Aloqaily & Nabil Mlaiki, 2023. "Integral Equation via Fixed Point Theorems on a New Type of Convex Contraction in b -Metric and 2-Metric Spaces," Mathematics, MDPI, vol. 11(2), pages 1-18, January.

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