Abstract:
In this paper, we present some fixed point results for a generalized
class of nonexpansive mappings in the framework of uniformly convex hyperbolic space and also propose a new iterative scheme for approximating the fixed
point of this class of mappings in the framework of uniformly convex hyperbolic
spaces. Furthermore, we establish some basic properties and some strong and
4-convergence theorems for these mappings in uniformly convex hyperbolic
spaces. Finally, we present an application to the nonlinear integral equation
and also, a numerical example to illustrate our main result and then display the
efficiency of the proposed algorithm compared to different iterative algorithms
in the literature with different choices of parameters and initial guesses. The
results obtained in this paper extends and generalize corresponding results in
uniformly convex Banach spaces, CAT(0) spaces and other related results in
literature.
