Advances in Analysis
Fixed Point Approximations with Finite Relatively Nonexpansive Maps in Some Real Banach Spaces
Download PDF (560.3 KB) PP. 19 - 29 Pub. Date: January 15, 2017
Author(s)
- Umar Yusuf Batsari*
Department of Mathematics and Statistics, Hassan Usman Katsina Polytechnic, Katsina State, Nigeria
Abstract
Keywords
References
[1] C.E. Chidume, Applicable Functional Analysis, I.C.T.P publicaion section, Triesty(Italy), 2003.
[2] C. Zˇalinescu, Convex Analysis in General Vector Spaces, World Scientific River Edge, NJ, U.S.A, 2002.
[3] C. Zˇalinescu On Uniformly Convex Functions, J. Math. Anal. Appl. 95(1983) 344-374.
[4] E. Blum, W. Oettli, from Optimization and Variational Inequalities to equilibrium Problems, Math. Stud., 63(1994) 123-145.
[5] G.L. Acedo, H.K. Xu, Iterative Methods for Srict Pseudo-Contractions in Hilbert Spaces, Nonlinear Anal., 67(2007)2258-2271.
[6] H.K. Xu, Inequalities in Banach Spaces with Applications, Nonlinear Anal. 16(1991) 1127-1138.
[7] I. Cioranescu, Geometry of Banach Spaces, Duality Mappings and Nonlinear Problems, Kluwer, Dordrecht, 1990.
[8] P.C. Duan, J.Zhao, Strong Convergence Theorems by Hybrid Methods for Strict Pseudo-Contractions and Equilibrium Problems, FPTA, (2010), doi: 10.1155/2010/528307.
[9] P. Duan, Convergence Theorems Concerning Hybrid Methods for Strict Pseudo-Contractions and Systems of Equilibrium Problems, J. Ineq. Appl.(2010), doi: 1155/2010/396080. 2010
[10] P.L. Combettes, S.A. Hirstoaga, Equilibrium Programming in Hilbert Spaces, J. Nonlinear Convex Anal., 6(2005)117-136.
[11] S. Kamimura, W. Takahashi, Strong Convergence of a Proximal-Type Algorithm in a Banach Space, SIAM J. Optim. 13(2002) 938-945.
[12] S. S. Chang, Jong Kyu Kim and Xiong RuiWang.Modified Block Iterative Algorithm for Solving Convex Feasibility Problems in Banach Spaces.J. Ineq. Appl., Vol.2010, Article ID 869684, 14 pages, doi:101155/2010/869684.
[13] S.S. Zhang.Existence and Approximation of Solutions of Set-Valued Variational Inclusions in Banach Spaces. Appl. Math. Engl. Ed, 30(9), 1105-1112(2009), doi:10.1007/s10483-009-0904-6.
[14] V. Colao, G. Marino, H.K. Xu, An Iterative Method for Finding Common Solutions of Equilibrium and Fixed Point Problems, J. Math. Anal. Appl. 344(2008) 340-352.
[15] W. Takahashi, K. Zembayashi, Strong and Weak Convergence Theorems for Equilibrium Problems and Relatively Nonexpansive Mappings in Banach Spaces, Nonlinear Analysis(2008), doi: 10.1016/J.na.2007.11.031.
[16] W. Takahashi, Nonlinear Functional Analysis, Yokohama Publishers, Yokohama, 2000.
[17] Y.I. Alber, Metric and Generalised Projection Operator in Banach Spaces: Properties and Applications in : A.G. Karosatos(Ed.) Theory and Applications of Nonlinear Operaors of Accretive and Monotone Type, Marcel Dekker, New York, 1996, pp.15-50
[18] C. E. Chidume and S.A. Mutangadura An example of Mann iteration method fopr Lipschitz Pseudocontractions, Proc. Amer. Math. Soc. 129(8) (2001), 2359-2369.
[19] K. Nakajo, K. Shimoji and W. Takahashi, Strong convergence theorems by the hybrid method for families of nonexpansive mappings in Hilbert spaces, Taiwanese J. Math. 10(2) (2006), 339-360.
[20] T. H. Kim and W. Takahashi, Strong convergence of modified iteration process for relatively asymptotically nonexpansive mappings, Taiwanese J. Math. 14(6) (2010), 2163-2180.
[21] Umar Yusuf Batsari, Fixed Point Approximations and Solutions of Nonlinear Equilibrium Problems in Uniformly Smooth and Uniformly Convex Real Banach Spaces, JPFPTA 9(3) (2014), 169-192. http://www.pphmj.com/journals/jpfta.htm.
[22] S. Matsushita and W. Takahashi. A Strong Convergence Theorem for Relatively Nonexpansive Mappings in Banach Space. Journal of Approximation Theory, 134(2005), 257-266.