Mixed type algorithms for a new iteration in hyperbolic spaces

Abstract

In fixed point theory, iterative methods are commonly employed to approximate fixed points of nonlinear mappings. In addition to the nonlinear mappings considered in fixed point theory, the nature of the underlying spaces also plays a crucial role. Numerous fixed point results and iterative algorithms for approximating fixed points of nonlinear mappings have been developed in spaces endowed with a convex structure. In this paper, a mixed type iteration process for approximating a common fixed point of two asymptotically nonexpansive mappings is discussed. A - convergence theorem under certain conditions is also established in a hyperbolic space framework. The equivalence of - convergence to Opial’s condition is utilised to establish the result.