Original new fixed point theorems in nth order G− metric spaces

Abstract

Many generalizations of the traditional metric space have been introduced in the literature, such as 2−, D−, G−, S− and b−metric spaces. When the studies on these generalized metric spaces are examined, it is seen that the main motivation of the researchers is to develop and generalize the famous Banach fixed point theorem. Although introduced with a similar motivation, its ability to measure the distance between n points simultaneously distinguishes the n th order G−metric space from other generalized metric spaces. In this study, we will give new and original fixed point theorems that reveal the importance of G−metric techniques since they cannot be reduced to the framework of quasi and conventional metric spaces.