Minimax Theory and its Applications 09 (2024), No. 2, 389--405
Copyright Heldermann Verlag 2024
A One-Step Tikhonov Regularization Iterative Scheme for Solving Split Feasibility and Fixed Point Problems
Simeon Reich
Department of Mathematics, The Technion -- Israel Institute of Technology, Haifa, Israel
sreich@technion.ac.il
Adeolu Taiwo
Department of Mathematics, The Technion -- Israel Institute of Technology, Haifa, Israel
taiwoa@campus.technion.ac.il
We study split feasibility and fixed point problems for Lipschitzian pseudocontractive and nonexpansive mappings in real Hilbert spaces. Using Tikhonov's regularization technique, we first propose an Ishikawa-type gradient-projection iterative scheme for approximating solutions to such problems and then carry out its convergence analysis. A weak convergence theorem is established, applications are derived, and several numerical examples are presented.
Keywords: Fixed point problem, Hilbert space, minimization problem, pseudocontractive mapping.
MSC: 47H10, 47H09, 47J25, 46N10.
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