Some Fixed Point Theorems in the Complex Valued Metric-Like Spaces

The main purpose of this article is to study fixed point theorem in the complex valued metric-like spaces. In this article, we prove that if (X, Delta) is a complete complex valued metric-like space and the mappings U, V : X -> X satisfy Delta(Ux, Vy) less than or similar to alpha Delta(x, y) + beta Delta(x, Ux)Delta(y, Vy)/1+Delta(x, y) for all x, y is an element of X, where alpha, beta are non-negative real numbers and alpha + beta < 1, then U and V have a unique common fixed point. Another main result of this article reads as follows. Let (X, Delta) be a complete complex valued metric-like space and let V : X -> X be a map such that Delta(Vx, Vy) less than or similar to Delta(x, y) - phi(Delta(x, y)) for all x, y is an element of X, where phi : C greater than or similar to 0 -> C greater than or similar to 0 is a non-decreasing continuous function such that phi(z) = 0 if and only if z = 0. Then, V has a unique fixed point. Some other related results are also discussed.