Double Controlled Metric Type Spaces and Some Fixed Point Results

In this article, in the sequel of extending b-metric spaces, we modify controlled metric type spaces via two control functions alpha (x, y) and mu(x, y) on the right-hand side of the b-triangle inequality, that is, d(x,y) <= alpha(x,z)d(x,z) + mu(z,y)d(z,y), for all x,y,z is an element of 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 phi-nonlinear type contractions in the setting of double controlled metric type spaces.