Inertial Shrinking Projection Algorithm for Relatively Nonexpansive Mappings

This paper introduces an inertial shrinking projection algorithm for approximating fixed points of relatively nonexpansive mappings in uniformly convex and smooth Banach spaces. By incorporating inertial terms, the method improves convergence speed and stability compared to classical projection techniques. The analysis relies on geometric properties such as the Kadec-Klee condition and the continuity of the duality mapping to ensure strong convergence. The proposed algorithm generalizes several existing iterative schemes and operates under mild assumptions. Numerical results in both finite-dimensional and function spaces confirm its practical effectiveness.

کلیدواژه ها:

Inertial algorithm ، Relatively nonexpansive maps ، Generalized projection ، strong convergence