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The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which is weak relatively nonexpansive mapping but not relatively nonexpansive mapping in Banach space l2. Our results improve and extend the corresponding results announced in [W. Takahashi and K. Zembayashi, Strong convergence theorem by a new hybrid method for equilibrium problems and relatively nonexpansive mappings, Fixed Point Theory Appl. (2008), Article ID 528476, 11 pages; doi:10.1155/2008/528476] and [Y. Su, Z. Wang,and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009), no.
11, 5616–5628] and some other papers.
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참고문헌 (24)
참고문헌 신청
B. Halpern / 1967 / Fixed points of nonexpanding maps / Bull. Amer. Math. Soc. 73 : 957 ~ 961
D. Butnariu / 1997 / Iterative averaging of entropic projections for solving stochastic convex feasibility problems / Comput. Optim. Appl. 8 (1) : 21 ~ 39
D. Butnariu / 2000 / Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization / Kluwer Academic Publishers
D. Butnariu / 2001 / Asymptotic behavior of relatively nonexpansive operators in Banach spaces / J. Appl. Anal. 7 (2) : 151 ~ 174
E. Blum / 1994 / From optimization and variational inequalities to equilibrium problems / Math. Student 63 (1) : 123 ~ 145
D. Butnariu / 1997 / Iterative averaging of entropic projections for solving stochastic convex feasibility problems / Comput. Optim. Appl. 8 (1) : 21 ~ 39
D. Butnariu / 2000 / Totally Convex Functions for Fixed Points Computation and Infinite Dimensional Optimization / Kluwer Academic Publishers
D. Butnariu / 2001 / Asymptotic behavior of relatively nonexpansive operators in Banach spaces / J. Appl. Anal. 7 (2) : 151 ~ 174
E. Blum / 1994 / From optimization and variational inequalities to equilibrium problems / Math. Student 63 (1) : 123 ~ 145
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