A New Extension of CJ Metric Spaces—Partially Controlled J Metric Spaces

Abstract

This article introduces the concept of partially controlled J metric spaces; in particular, the J metric space with self-distance is not necessarily zero, which is important in computer science. We prove the existence of a unique fixed point for linear and nonlinear contractions, provide some examples to prove the existence of this metric space, and present some important applications in fractional differential equations, i.e., “Riemann–Liouville derivatives”.

On some fixed point results using CG simulation functions via w-distance with applications

“…In the realm of metric fixed points, Banach pioneered the renowned Banach's contraction principle [1] , a cornerstone method pivotal for establishing the existence and uniqueness of solutions to a multitude of problems in mathematical analysis. Subsequently, a plethora of researchers have contributed by extending and enhancing the Banach contraction principle in diverse directions and spaces, as exemplified in works such as [2] , [3] , [4] , [5] , [6] , [7] , [8] , [9] , [10] , [11] , [12] , [13] , [14] . Subsequently, Kada et al [15] delved into the realm of metric spaces, introducing the concept of w -distance mappings and establishing significant fixed-point results.…”