abstract 102

Bulletin of Computational Applied Mathematics (Bull CompAMa) 

102

Fixed point theorem for two functions on a hyperbolic value metric space (Research Paper)

Wilmer Barrera.

The fixed point theory is one of the most important tools in nonlinear analysis because it provides theorems that solve problems across various branches of mathematics such as differential equations, game theory, and fractal theory. A hyperbolic number is an element z=x+ky, where x, y are real numbers and k is a non-real unit called a hyperbolic unit that satisfies k2=1. The set of hyperbolic numbers is denoted by H. This system of numbers becomes a commutative ring with two specific operations defined on it. Also, it is possible to define a partial ordering on this set. So, in this paper we will work with a hyperbolic-valued metric dH defined on any non-empty set X. In this paper, we present a theorem that guarantees existence and uniqueness of common fixed point for two functions defined on a complete hyperbolic value metric space.

Keywords: Common fixed point; commutative functions; hyperbolic numbers; hyperbolic value metric space; complete hyperbolic value metric space.

Cite this paper:

Barrera W.

Fixed point theorem for two functions on a hyperbolic value metric space,

Bull. Comput. Appl. Math. (Bull CompAMa),

Vol. 12, No.2 pp.xx-xx, 2024.