The aim of this paper is to prove the existence and uniqueness of fixed point for (j-f)-weak contraction mappings and (y−f)-weak contraction mappings in a complete and Hausdorff generalized metric space.

Best proximity point theorems for self-mappings were investigated with different conditions on spaces for contraction mappings. In this paper, we prove best proximity point theorems for proximal F∗,-weak contraction mappings.

The purpose of this paper is to  nd of the theoretical results of  xed point theorems for a mixed monotone mapping in a metric space endowed with partially order by using the generalized Kanann type contractivity of assumption. Also, as an application, we prove the existence and uniqueness of solution for a  rst{order ordinary di erential equation with periodic boundary conditions admitting only the existence of a mixed -solution.

Endpoint results are presented for multi{valued cyclic contraction mappings on complete metric spaces (X; d). Our results extend previous results given by Nadler (1969), Da er{Kaneko (1995), Harandi (2010), Moradi and Kojasteh (2012) and Karapinar (2011).