F-convex contraction via admissible mapping and related fixed point theorems with an application

Y. Mahendra Singh, Mohammad Khan, Shin Min Kang

Research output: Contribution to journalArticle

3 Citations (Scopus)

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 Istrăţescu [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.

Original languageEnglish
Article number105
JournalMathematics
Volume6
Issue number6
DOIs
Publication statusPublished - Jun 20 2018

Keywords

  • Fixed point
  • Non-linear Fredholm integral equation
  • α*-admissibleαF-contraction
  • α-admissible mapping
  • α-F-convex contraction

ASJC Scopus subject areas

  • Mathematics(all)

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