New best proximity point results in G-metric space

Best approximation results provide an approximate solution to the xed point equation Tx = x, when the non-self mapping T has no xed point. In particular, a well- known best approximation theorem, due to Fan [6], asserts that if K is a nonempty compact convex subset of a Hausdor locally convex topological vector space E and T : K ! E is a continuous mapping, then there exists an element x satisfying the condition d(x; Tx) = inffd(y; Tx) : y 2 Kg, where d is a metric on E. Recently, Hussain et al. (Abstract and Applied Analysis, Vol. 2014, Article ID 837943) introduced proximal contractive mappings and established certain best proximity point results for these mappings in G-metric spaces. The aim of this paper is to introduce certain new classes of auxiliary functions and proximal contraction mappings and establish best proximity point theorems for such kind of mappings in G-metric spaces. As consequences of these results, we deduce certain new best proximity and xed point results in G-metric spaces. Moreover, we present certain examples to illustrate the usability of the obtained results.