Double controlled metric type spaces and some fixed point results

Abstract

In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions α(x, y) and μ(x, y) on the right-hand side of the b-triangle inequality, that is, d(x, y) ≤ α(x, z)d(x, z) + μ(z, y)d(z, y), for all x, y, z ∈ X. Some examples of a double controlled metric type space by two incomparable functions, which is not a controlled metric type by one of the given functions, are presented. We also provide some fixed point results involving Banach type, Kannan type and π-nonlinear type contractions in the setting of double controlled metric type spaces.