Fixed Point Results for Generalized (<i>α</i>, <i>β</i>)-Nonexpansive Type-1 Mapping in Hyperbolic Space

In this article, we define several fundamental characteristics and put forward some basic fixed point results in the context of hyperbolic space for generalized (α, β)-nonexpansive type-1 mappings. Additionally, we present ∆-convergence and strong convergence results within the framework of hyperbolic space for these types of mappings. Lastly, we provide some numerical examples to highlight our main result and comparison the iterative procedures that we use in our study with various iterative techniques from the literature. The results in this study enhance, broaden and unite corresponding results in the literature.