In this paper, we establish new convergence theorems and best proximity point theorems for a pair of nonlinear non-self mappings in metric spaces. Mathematics Subject Classification: 41A17, 41A65

We establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an Ac -multimap or a multimap T : A → 2 such that both T and S ◦ T are closed and have the KKM property for each Kakutani multimap S : B → 2. As applications, we obtain existence theorems of equilibrium pairs for free n-person games as well as...

‎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 present a novel approximate algorithm to calculate the top-k closest pairs join query of two large and high dimensional data sets. The algorithm has worst case time complexity OðdnkÞ and space complexity OðndÞ and guarantees a solution within a Oðd1þ1tÞ factor of the exact one, where t 2 {1,2, . . . ,1} denotes the Minkowski metrics Lt of interest and d the dimensionality. It m...