On the g-best proximity point results for G-generalized proximal contraction mappings in G-metric spaces

Abstract

In this paper, we introduce the notion of G-generalized proximal contraction mappings of first kind and second kind with respect to a mapping g in a G-metric space and establish some g-best proximity point theorems for such kind of nonself mappings in this space. Moreover, we present some examples to support the results proved herein. To the best of our knowledge, no results are known at the moment for this kind of mappings in G-metric spaces. Our results even without the mapping g are new. Some results in the existing literature are also generalized by our results.