(untitled) (European Journal of Pure and Applied Mathematics, 2025)
The notion of generalized metric, more commonly known as the rectangular metric, was introduced by Branciari in 2000, replacing the triangle inequality of metric spaces by the so-called rectangular inequality. In this paper we further generalize this notion by adding two more terms to the right-hand side of the rectangular inequality. We study basic properties of spaces endowed by such distance functions, and prove the modified versions of Banach and Kannan fixed point theorems on these spaces. The results are substantiated by examples. Finally, we state some open problems related to topological structure and fixed point theory on generalized Branciari metric spaces.