A system of general nonlinear variational inclusions in Banach spaces

doi:10.1007/s10483-015-2001-6

Abstract

Abstract: A new system of general nonlinear variational inclusions is introduced and studied in Banach spaces. An iterative algorithm is developed and analyzed by use of the resolvent operator techniques to find the approximate solutions of the system of general nonlinear variational inclusions involving different nonlinear operators in uniformly smooth Banach spaces.

Key words: system of general nonlinear variational inclusions, uniformly smooth Banach space, strongly accretive mapping, resolvent operator, relaxed accretive mapping

2010 MSC Number:

O177.91
O224

Xieping DING, SALAHUDDIN. A system of general nonlinear variational inclusions in Banach spaces. Applied Mathematics and Mechanics (English Edition), 2015, 36(12): 1663-1672.

TrendMD

References

[1] Baiocchi, C. and Capelo, A. Variational and Quasi Variational Inequalities, Applications to Free Boundary Problems, John Wiley and Sons, New York(1984)
[2] Brézis, H. Opérateurs Maximaux Monotone er Semi-Groupes de Contractions dans les Espaces de Hilbert, North-Holland, Amsterdam(1973)
[3] Zeidler, D. Nonlinear Functional Analysis and Its Applications II, Monotone Operators, Springer, Berlin(1985)
[4] Giannessi, F. Vector Variational Inequalities and Vector Equilibriua, Mathematics Theories, Kluwer Academic Publishers, London(2000)
[5] Verma, R. U. On a new system of nonlinear variational inequalities and associated iterative algorithms. Mathematical Sciences Research Hotline, 3, 65-68(1999)
[6] Verma, R. U. Iterative algorithms and a new system of nonlinear quasivariational inequalities. Advances in Nonlinear Variational Inequalities, 4, 117-124(2001)
[7] Kim, J. K. and Kim, D. S. A new system of generalized nonlinear mixed variational inequalities in Hilbert spaces. Journal of Convex Analysis, 11, 235-243(2004)
[8] Fang, Y. P., Huang, N. J., and Thompson, H. B. A new system of variational inclusions with(H, η)-monotone operators in Hilbert spaces. Computers and Mathematics with Applications, 49, 365-374(2005)
[9] Ding, X. P. and Feng, H. R. Algorithm for solving a new class of generalized nonlinear implicit quasi-variational inclusions in Banach spaces. Applied Mathematics and Computation, 208, 547-555(2009)
[10] Feng, H. R. and Ding, X. P. A new system of generalized nonlinear quasi-variational-like inclusions with A-monotone operators in Banach spaces. Journal of Computational and Applied Mathematics, 225, 365-373(2009)
[11] Ding, X. P. and Wang, Z. B. System of set-valued mixed quasi-variational-like inclusions involving H-η-monotone operators in Banach spaces. Applied Mathematics and Mechanics(English Edition), 30, 1-12(2009) DOI 10.1007/s10483-009-0101-z
[12] Wang, Z. B. and Ding, X. P.(H(·, ·), η)-accretive operators with an application for solving setvalued variational inclusions in Banach Spaces. Computers and Mathematics with Applications, 59, 1559-1567(2010)
[13] Ding, X. P. Sensitivity analysis for a system of generalized mixed implicit equilibrium problems in uniformly smooth Banach spaces. Nonlinear Analysis:Theory, Methods and Applications, 73, 1264-1276(2010)
[14] Ding, X. P. and Wang, Z. B. Auxiliary principle and algorithm for a system of generalized setvalued mixed variational-like inequality problems in Banach spaces. Journal of Computational and Applied Mathematics, 223, 2876-2883(2010)
[15] Ding, X. P. Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces. Applied Mathematics and Mechanics(English Edition), 31, 1049-1062(2010) DOI 10.1007/s10483-010-1341-z
[16] Suantai, S. and Petrot, N. Existence and stability of iterative algorithms for the system of nonlinear quasi mixed equilibrium problems. Applied Mathematics Letters, 24, 308-313(2011)
[17] Ding, X. P. Auxiliary principle and approximation solvability for system of new generalized mixed equilibrium problems in reflexive Banach spaces. Applied Mathematics and Mechanics(English Edition), 32(2), 231-240(2011) DOI 10.1007/s10483-011-1409-9
[18] Ding, X. P. Auxiliary principle and iterative algorithm for a new system of generalized mixed equilibrium problems in Banach spaces. Applied Mathematics and Computation, 218, 3507-3514(2011)
[19] Ding, X. P. Approximation solvability of system of generalized mixed implicit equilibrium problems in Banach spaces. Journal of Sichuan Normal University(Natural Science), 34, 1-9(2011)
[20] Ding, X. P. and Ho, J. L. New iterative algorithm for solving a system of generalized mixed implicit equilibrium problems in Banach spaces. Taiwanese Journal of Mathematics, 15, 673-694(2011)
[21] Agarwal, R. P., Cho, Y. J., and Petrot, N. System of general nonlinear set valued mixed variational inequality problems in Hilbert spaces. Fixed Point Theory and Applications, 31, 31(2011)
[22] Suantai, S. and Petrot, N. Existence and stability of iterative algorithms for the system of nonlinear quasi mixed equilibrium problems. Applied Mathematics Letters, 24, 308-313(2011)
[23] Ding, X. P. Iterative algorithm of solutions for a system of generalized mixed equilibrium problems in reflexive Banach spaces. Applied Mathematics and Computation, 218, 4953-4961(2012)
[24] Ding, X. P. Auxiliary principle and algorithm of solutions for a new system of generalized mixed equilibrium problems in Banach spaces. Journal of Optimization Theory and Applications, 155, 796-809(2012)
[25] Ahmad, M. K. and Salahuddin, S. A stable perturbed algorithms for a new class of generalized nonlinear implicit quasi variational inclusions in Banach spaces. Advances in Pure Mathematics, 2, 139-148(2012)
[26] Huang, N. J. and Fang, Y. P. Generalized m-accretive mappings in Banach spaces. Journal of Sichuan University, 38, 591-592(2001)
[27] Lan, H. Y., Cho, Y. J., and Verma, R. U. Nonlinear relaxed cocoercive variational inclusions involving(A, η)-accretive mappings in Banach spaces. Computers and Mathematics with Applications, 51, 1529-1538(2006)
[28] Weng, X. L. Fixed point iteration for local strictly pseudo contractive mapping. Proceedings of the American Mathematical Society, 113, 727-737(1991)
[29] Xu, H. K. Inequqlities in Banach spaces with applications. Nonlinear Analysis:Theory, Methods and Applications, 16, 1127-1138(1991)