Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application

Abstract

In this paper, we discuss the existence and uniqueness of common fixed-point theorems satisfying implicit relations on 2-cone Banach spaces. Modifying obtained new contractive conditions, we also give an application to the fixed-circle problem.

Bilateral-type solutions to the fixed-circle problem with rectified linear units application

“…were investigated in rectangular and quasi metric spaces (see [1,2]). Using known fixed-point techniques, some applications were presented to "Fixed-Circle Problem" on 2-cone Banach spaces, M b -metric spaces, rectangular M -metric spaces and parametric N b -metric spaces (see [6,13,19,29]). In some of the above studies, some open problems were left to improve fixed-circle problem.…”

Existence of Fixed Point Theorems in a Linear 2-Normed Spaces

“…Here after, many authors establish the fixed point theorem in 2-normed spaces and 2-Banach spaces, See [4,6,[16][17][18][19][20]. Recently, generalise the concept of 2-normed space as well as 2-Banach space into 2-cone Banach space [3,12,22]. We now state some definitions before presenting our main results.…”