Inertial Halpern-type method for solving split feasibility and fixed point problems via dynamical stepsize in real Banach spaces
Godwin Chidi Ugwunnadi, Hammed Anuoluwapo Abass, Maggie Aphane, Olawale Kazeem Oyewole · ANNALI DELL UNIVERSITA DI FERRARA · 2023
Abstract In this paper, we introduce a modified Halpern inertial method for approximating solutions of split feasibility problem and fixed point problem of Bregman strongly nonexpansive mappings in the framework of p-uniformly convex and uniformly smooth real Banach spaces. We establish a strong convergence result for the sequence generated by our iterative scheme under some mild conditions without the computation of the operator norm. We state some consequences and present some examples to show the efficiency and implementation of our proposed method. The result discussed in this paper extends and generalizes many recent results in this direction. Our result extends and complements some related results in literature.