Fixed point and common fixed point theorems for (γ, s, q)-F-contraction mappings in b-metric like spaces with application

Abstract

This paper proves some fixed point theorems for (γ, s, q)-F -Kannan mappings and a common fixed point theorem for (γ, s, q)-F -Reich type contraction mappings in a b-metric like space. Finally, we give an application to the solvability of a nonlinear integral equation.Theorem 1.2. [37] Let Υ be a complete metric space with metric d, and let µ : Υ → Υ be a function with the following property: (3) d(µι, µκ) ≤ ad(ι, µι) + bd(κ, µκ) + cd(ι, κ), for all ι, κ ∈ Υ where a, b, c are nonnegative and satisfy a + b + c < 1. Then µ has a unique fixed point.