A Common Fixed Point Theorem for Two Functions Defined on a Hyperbolic Value Metric Space

The fixed point theory is one of the most important and powerful 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 \(k^2=1\) . The set of hyperbolic numbers is denoted by \(\mathbb {H}\) . This mathematical structure is a commutative ring and also has a partial ordering. So, this allows us to define a hyperbolic value metric \(d_{\mathbb {H}}\) on any non-empty set X. In this paper, we present some ideas to obtain a common fixed point for two functions defined on a hyperbolic value metric space \((X,d_{\mathbb {H}})\) .