Some fixed point theorems for ( ψ − ϕ ) $(\psi -\phi )$ -almost weak contractions in S-metric spaces solving conformable differential equations

Abstract

Abstract The aim of this paper is to establish some fixed point and common fixed point theorems for ( ψ − ϕ ) $(\psi -\phi )$ -almost weak contractions in complete S-metric spaces, followed by some supportive examples. Our results extend and generalize several results existing in the literature. We employ the outcomes of the fixed point theorems to establish the existence and uniqueness of a solution for a class of conformable differential equations which is a new branch of fractional calculus.

Keywords

• Fixed point
• Common fixed point
• ( ψ − ϕ ) $(\psi -\phi )$ -almost weak contraction
• S-metric space