Version 1
: Received: 6 October 2024 / Approved: 7 October 2024 / Online: 7 October 2024 (11:33:51 CEST)
How to cite:
Berinde, V.; Saleh, K. An Averaged Halpern Type Algorithm for Solving Fixed Point Problems and Variational Inequality Problems. Preprints2024, 2024100408. https://doi.org/10.20944/preprints202410.0408.v1
Berinde, V.; Saleh, K. An Averaged Halpern Type Algorithm for Solving Fixed Point Problems and Variational Inequality Problems. Preprints 2024, 2024100408. https://doi.org/10.20944/preprints202410.0408.v1
Berinde, V.; Saleh, K. An Averaged Halpern Type Algorithm for Solving Fixed Point Problems and Variational Inequality Problems. Preprints2024, 2024100408. https://doi.org/10.20944/preprints202410.0408.v1
APA Style
Berinde, V., & Saleh, K. (2024). An Averaged Halpern Type Algorithm for Solving Fixed Point Problems and Variational Inequality Problems. Preprints. https://doi.org/10.20944/preprints202410.0408.v1
Chicago/Turabian Style
Berinde, V. and Khairul Saleh. 2024 "An Averaged Halpern Type Algorithm for Solving Fixed Point Problems and Variational Inequality Problems" Preprints. https://doi.org/10.20944/preprints202410.0408.v1
Abstract
In this paper we propose and study in the setting of a Hilbert space an averaged Halpern type algorithm for approximating the solution of a common fixed point problem for a couple of nonexpansive and demicontractive mappings with a variational inequality constraint. The strong convergence of the sequence generated by the algorithm is established under feasible assumptions on the parameters involved. In particular, we also obtain the common solution of the fixed point problem for nonexpansive or demicontractive mappings and of a variational inequality problem. Our results extend and generalize various important related results in literature that were established for the pairs (nonexpansive, nonspreading) or (nonexpansive, strongly quasi-nonexpansive) mappings. Numerical tests to illustrate the superiority of our algorithm over the ones existing in literature are also reported.
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
