Relational Contractions Involving (c)-Comparison Functions with Applications to Boundary Value Problems

After the introduction of Alam–Imdad’s relation-theoretic contraction principle, the field of metric fixed point theory has attracted much attention. A number of fixed point theorems in the context of relational metric space employing various types of contractions has been appeared during the last seven years. In this manuscript, one proved a metrical fixed point theorem for ϕ-contraction involving (c)-comparison functions employing an amorphous relation. The result proved in this paper refines, modifies, unifies and sharpens several existing fixed point results. We also constructed an example in order to attest the credibility of our results. Finally, we applied our result to establish the existence and uniqueness of solution of certain periodic boundary value problem.