DOI: 10.24193/fpt-ro.2025.2.09

Authors: Mohammad Eslamian

Abstract: A class of nonlinear mappings in p-uniformly convex and uniformly smooth Banach spaces is proposed. We call each mapping in this class a strict pseudo-contraction type mapping. This class contains the classes of strict pseudo-contraction mappings in Hilbert spaces and metric resolvents of maximal monotone operators in Banach spaces. Then, we study the split common fixed point problem for a finite family of strict pseudo-contraction-type mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an inertial Halpern-type algorithm with the step size independent on the prior estimate of the norm of the bounded linear operator and prove strong convergence theorem.

Key Words and Phrases: Split common fixed point problem, strict pseudo-contraction, inertial algorithm.

2010 Mathematics Subject Classification: 47H05, 47H09, 47J25, 47H10.

Published on-line: May 1st, 2025.

Fulltext pdf

Back to volume's table of contents