‎In this paper‎, ‎first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points‎. ‎Finally‎, ‎as consequences of these theorems‎, ‎we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces‎. ‎We present an ex...

In this paper, we establish some new existence and convergence theorems of iterates of best proximity points on quasiordered metric spaces. Some applications to the fixed point theory are also given. Our results generalize and improve some known results in the literature. MSC: 41A50, 47H09, 47H10

In this paper we present some best proximity point theorems for a combination of weak Kannan and Chatterjea nonlinear cyclic contraction and the MT functions in the frameworks of a metric space (X, d), thereby furnishing an optimal approximate solution to the equations of the form Tx = x, where T is a non-self mapping.

We find a priori and a posteriori error estimates of the best proximity point for the Picard iteration associated to a cyclic contraction map, which is defined on a uniformly convex Banach space with modulus of convexity of power type.

In this paper, we present best proximity point theorems for new class ofK−rational proximal contraction, in the setting of metric spaces. Some illustrative example are also given.