The purpose of this article is to first introduce the notion of tripled best proximity point and cyclic contraction pair. We also establish the existence and convergence theorems of tripled best proximity points in metric spaces. Moreover, we apply our results to setting of uniformly convex Banach space. Finally, we obtain some results on the existence and convergence of tripled fixed point in ...

In this presentation, we discuss an intuitive model of the kinematics and dynamics of spatial compliant contact. The kinematic model gives a relation between the relative velocity of two rigid bodies and the velocities of two points on their surfaces that have smallest distance. The dynamic model uses a 6D spatial spring element to model the elastic forces between the bodies resulting from the ...

‎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...

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

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

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.