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A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings Cover

A new fixed point technique for equilibrium problem with a finite family of multivalued quasi-nonexpansive mappings

By: T.M.M. Sow  
Open Access
|Nov 2023

References

  1. V. Berinde, M. Pacurar, The role of the Pompeiu-Hausdorff metric in fixed point theory, Creat. Math. Inform., vol. 22, no. 2, 2013, 143-150.
  2. E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, vol. 63, 1994, 123-145.
  3. P. L. Combettes, S. A. Hirstoaga, Equilibrium programming in Hilbert spaces, Journal of Nonlinear and Convex Analysis, vol.6, no.1, 2005, 117-136.
  4. P. Cholamjiak, W. Cholamjiak, S. Suantai, Viscosity approximation methods for nonexpansive multi-valued nonself mapping and equilibrium problem, Demon-stratio Mathematica, vol. XLVII, no. 2, 2014.
  5. S. Chang, Y. Tang, L. Wang, G. Wang, Convergence theorems for some multi-valued generalized nonexpansive mappings, Fixed Point Theory and Applications, vol. 33, no. 1, 2014.
  6. C. E. Chidume, Geometric Properties of Banach Spaces and Nonlinear iterations, Lectures Notes in Mathematics (vol. 1965), Springer, London, UK, 2009.
  7. K. Fan, A minimax inequality and applications, in Inequalities III, (O. Shisha, ed.), Academic Press, New York, 1972.
  8. F.O. Isiogugu, M. O. Osilike, Convergence theorems for new classes of multivalued hemicontractive-type mappings, Fixed Point Theory and Applications, vol. 93, 2014.
  9. P. E. Mainge, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Analysis, vol. 16, 2008, 899-912.
  10. G. J. Minty, Monotone (nonlinear) operator in Hilbert space, Duke Math., vol. 29, 1962, 341-346.
  11. A. Moudafi, Viscosity approximation methods for fixed point problems, J. Math. Anal. Appl., vol. 241, 2000, 46-55.
  12. Jr. Nadla, Multivaled contraction mappings, Pacific J. Math.,vol. 30, 1969, 475-488.
  13. J. F. Nash, Non-coperative games, Annals of Mathematics, second series, vol. 54, 1951, 286-295.
  14. J. F. Nash, Equilibrium points in n-person games, Proceedings of the National Academy of Sciences of the United States of America, vol. 36, no. 1, 1950, 48-49.
  15. B. Panyanak, Mann and Ishikawa iteration processes for multi-valued mappings in Banach Spaces, Comput. Math. Appl., vol. 54, 2007, 872-877.
  16. N. Petrot, K. Wattanawitoon, P. Kumam, A hybrid projection method for generalized mixed equilibrium problems and fixed point problems in Banach spaces, Nonlinear Analysis, Hybrid Systems, vol. 4, 2010, 631-643.
  17. D. N. Qu, C. Z. Cheng, A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space, Fixed Point Theory and Applications, vol. 2011, article 17, 2011.
  18. Y. Song, Y. J. Cho, Some notes on Ishikawa iteration for multi-valued mappings, Bull. Korean Math. Soc., vol. 48, no. 3, 2011, 575-584.
  19. M. Sene, P. Faye, N. Djitté, A Krasnoselskii type Algorithm approximating a common Fixed Point of a finite family of multivalued strictly pseudo-contractive mappings in Hilbert spaces, J. Maths. Sci. Adv. Appl., vol. 27, 2014, 59-80.
  20. P. Sunthrayuth, P. Kumam, A new computational technique for common solutions between systems of generalized mixed equilibrium and fixed point problems, Journal of Applied Mathematics, Article ID 230392, 2013, 17 pages.
  21. H. K. Xu, A variable Krasnoselskii-Mann algorithm and the multiple set split feasibility problem, Inverse Problem, vol. 26, 2006, 2021-2034.
  22. H. K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., vol. 66, no. 2, 2002, 240-256.
DOI: https://doi.org/10.2478/gm-2022-0009 | Journal eISSN: 1584-3289 | Journal ISSN: 1221-5023
Language: English
Page range: 119 - 134
Submitted on: Oct 18, 2019
Accepted on: Nov 9, 2022
Published on: Nov 24, 2023
Published by: Lucian Blaga University of Sibiu
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year

© 2023 T.M.M. Sow, published by Lucian Blaga University of Sibiu
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.