Convergence To Approximate Solutions of Multivalued Operators

Main Article Content

Zena Hussein Maibed

Abstract

The goal of this study is to provide a new explicit iterative process method  approach for solving maximal monotone(M.M )operators in Hilbert spaces utilizing a finite family of different types of  mappings as( nonexpansive mappings,resolvent mappings and projection mappings. The findings given in this research strengthen and extend key previous findings in the literature. Then, utilizing various structural conditions in Hilbert space and variational inequality problems, we examine the strong convergence to nearest point projection for these explicit iterative process methods Under the presence of two important conditions for convergence, namely closure and convexity. The findings reported in this research strengthen and extend key previous findings from the literature

Article Details

How to Cite
Convergence To Approximate Solutions of Multivalued Operators . (2023). Ibn AL-Haitham Journal For Pure and Applied Sciences, 36(2), 367-374. https://doi.org/10.30526/36.2.3023
Section
Mathematics

How to Cite

Convergence To Approximate Solutions of Multivalued Operators . (2023). Ibn AL-Haitham Journal For Pure and Applied Sciences, 36(2), 367-374. https://doi.org/10.30526/36.2.3023

References

. Bruck, E., A Strongly Convergent Iterative Solution for a Maximal Monotone Operator in

Hilbert Space, J. Math. Anal. Appl. 1974,48,114 -126 .

Rockafellar, T., Monotone Operator and The Proximal Point Algorithm, SIAM J. Control Optim. 1976, 14,877 – 898.

Rockafellar.T., Monotone Operators and Proximal Point Algorithm, SIAM J. Control Optim., 1976,14 ,887-897.

Fattorini,O. , Infinite-dimensional Optimaization and Control Theory, Cambridge

University Press, Cambrige, 1999.

Moudafi. A., Viscosity Approximation Methods for Fixed-Point Proplems, J. Math. Anal. Appl. 2000, 241, 46-55,.

Hugh. R.; Malik, P.; Kumar, V. On a New Faster Implicit Fixed Point Iterative Scheme inConvex Metric Space . J. Funct. Spaces 2015.

Khan,R.; Kumar, V.;Nawal, S.; Chugh, R., Random Iterative Algorithms and Almost SureStability in Banach Space, Filomat,2017, 31, 3611-3626.

Kumar, V.; Hussain, N.; Malik, P.; Chugh, R.Jungck-Type Implicit Iterative Algorithms with

Numerical Example , Filomat, 2017,31, 2303-2320.

Zena ,M ; Alaa, A, On The Convergence of New Iteration Schemes by Resolvent ZA-Jungck mapping,Journal of Interdisciplinary Mathematics, to appear, 2022.

Maibed , H. ; Hussein, S. , Approximation Fixed Point Theorems Via Generalized Like Contraction Mappings, AIP Conference Proceedings 2022, 2398, 060081.

Dadashi, V.;Postolache, M. Forward-Backward Splitting Algorithms for Fixed Point Problems and Zeros of the Sum of Monotone Operators, Arab. J. Math. 2019, 1-11.

Maibed, Z. ; Thajil, A, Zenali Iteration Method For Approximating Fixed Point of ZA – Quasi Contractive mappings, Haitham Journal for Pure and Applied Science, Oct 20, 2021.

Jamil ,Z. ; Abed, B., On A Modified SP-Iterative Scheme for Approximating Fixed Point of A Contraction Mapping, Iraqi Journal of Scienceno. 2015, 56, 4B, 3230-3239,June.

Boikanyo. A. and Morosanu G., A Contraction Proximal Point Algorithm with Two Monotone Operators, Nonlinear Anal. (TMA), 2019, 75, 5686-5692.

Cholamjiak, P.;Suparat, K., P. Nattawut, Weak and strong convergence theorems for the Inclusion Problems and Fixed Point of Nonexpansive Mappings, Mathematics , (MDPI), 2019, 7(167).

Jong ,K. ; Truong ,M.New Iterative Methods for Finding a Common Zero of a Finite Familiy of Monotone Operators in Hilbert Space, Bull. Korean Math. Soc. 2017, 54 ,4, 1347-1359,

Xu.K., Viscosity Approximations Method for Nonexpansive Mappings, J. Math. Anal. Appl. 2004, 298, 1, 279-291.

Chang ,S. On Chidume's open Equestions and Approximate Solutions of Multivalued Strongly Accretive Mapping Equations in Banach Space, J. Math. Anal. Appl 1997, 216, 1, 94-111.

Xu, G.,Weak and Strong Convergence Theorems for Strict Pseudo-Contraction in Hilbert Space , J. Math. Anal. Appl. 2017,329, 336-346.

Suzuki, T.,Strong Convergence of Krasnoselskii and Mann's Type Sequences for One-Parameter Nonexpansive Semigroups without Bochner Integrals, J. Math. Anal. Appl. 2005, 305, 227-239.