Axioms (Sep 2023)

Almost Boyd-Wong Type Contractions under Binary Relations with Applications to Boundary Value Problems

  • Amal F. Alharbi,
  • Faizan Ahmad Khan

DOI
https://doi.org/10.3390/axioms12090896
Journal volume & issue
Vol. 12, no. 9
p. 896

Abstract

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This article is devoted to investigating the fixed point theorems for a new contracitivity contraction, which combines the idea involved in Boyd-Wong contractions, strict almost contractions and relational contractions. Our results improve and expand existing fixed point theorems of literature. In process, we deduce a metrical fixed point theorem for strict almost Boyd-Wong contractions. To demonstrate the credibility of our results, we present a number of a few examples. Applying our findings, we find a unique solution to a particular periodic boundary value problem.

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