Relation-theoretic almost ϕ-contractions with an application to elastic beam equations

Abstract

In this article, we prove some results on existence and uniqueness of fixed points for an almost $ \phi $-contraction mapping defined on a metric space endowed with an amorphous relation. Our results generalize and improve several well known fixed point theorems of the existing literature. To substantiate the credibility of our results, we construct some examples. We also apply our results to determine a unique solution of a boundary value problem associated with nonlinear elastic beam equations.

Keywords

• almost contractions
• boundary value problems
• fixed points
• binary relations