New averaged type algorithms for solving split common fixed-point problem for demicontractive mappings

Vasile Berinde; Khairul Saleh

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arXiv · 2406.15366

New averaged type algorithms for solving split common fixed-point problem for demicontractive mappings

Vasile Berinde·Khairul Saleh

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Abstract

In this paper we propose new averaged iterative algorithms designed for solving a split common fixed-point problem in the class of demicontractive mappings. The algorithms are obtained by inserting an averaged term into the algorithms used in [Li, R. and He, Z., A new iterative algorithm for split solution problems of quasi-nonexpansive mappings {\it J. Inequal. Appl.} {\bf 131} (2015), 1--12.] for solving the same problem but in the class of quasi-nonexpansive mappings, which is a subclass of demicontractive mappings. Basically, our investigation is based on the embedding of demicontractive operators in the class of quasi-nonexpansive operators by means of averaged mappings. For the considered algorithms we prove weak and strong convergence theorems in the setting of a real Hilbert space and also provide examples to show that our results are effective generalizations of existing results in literature.

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BibTeX RIS

Vasile Berinde, Khairul Saleh. 2024-04-05. New averaged type algorithms for solving split common fixed-point problem for demicontractive mappings. https://arxiv.org/abs/2406.15366

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