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Oyewole, O. K.; Abass, H. A.; Mewomo, O. T.

A strong convergence algorithm for a fixed point constrained split null point problem. (English) Zbl 1522.47097

Rend. Circ. Mat. Palermo (2) 70, No. 1, 389-408 (2021).
Summary: In this paper, we introduce a new algorithm with self adaptive step-size for finding a common solution of a split feasibility problem and a fixed point problem in real Hilbert spaces. Motivated by the self adaptive step-size method, we incorporate the self adaptive step-size to overcome the difficulty of having to compute the operator norm in the proposed method. Under standard and mild assumption on the control sequences, we establish the strong convergence of the algorithm, obtain a common element in the solution set of a split feasibility problem for sum of two monotone operators and fixed point problem of a demimetric mapping. Numerical examples are presented to illustrate the performance and the behavior of our method. Our result extends, improves and unifies other results in the literature.

Cited in 31 Documents

MSC:

47J25 Iterative procedures involving nonlinear operators
47J22 Variational and other types of inclusions
47H05 Monotone operators and generalizations
49J35 Existence of solutions for minimax problems
90C47 Minimax problems in mathematical programming

Keywords:

monotone variational inclusion problem; monotone operator; demimetric mapping; strong convergence; real Hilbert space; split feasibility problem; fixed point problem; self adaptive step-size method
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References:

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