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In this paper, we first show that the iteration {xn} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {xn} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].
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참고문헌 (13)
참고문헌 신청
C. W. Groetsch / 1972 / A note on segmenting Mann iterates / J. Math. Anal. Appl 40 : 369 ~ 372
F. E. Browder / 1968 / Semicontractive and semiaccretive nonlinear mappings in Banach spaces / Bull. Amer. Math. Soc 74 : 660 ~ 665
H. F. Senter / 1974 / Approximating fixed points of nonexpansive mappings / Proc. Amer. Math. Soc 44 : 375 ~ 380
J. Schu / 1991 / Weak and strong convergence to fixed points of asymptotically nonexpansive mappings / Bull. Austral. Math. Soc 43 (1) : 153 ~ 159
K. K. Tan / 1993 / Approximating fixed points of nonexpansive mappings by the Ishikawa Iteration process / J. Math. Anal. Appl 178 (2) : 301 ~ 308
F. E. Browder / 1968 / Semicontractive and semiaccretive nonlinear mappings in Banach spaces / Bull. Amer. Math. Soc 74 : 660 ~ 665
H. F. Senter / 1974 / Approximating fixed points of nonexpansive mappings / Proc. Amer. Math. Soc 44 : 375 ~ 380
J. Schu / 1991 / Weak and strong convergence to fixed points of asymptotically nonexpansive mappings / Bull. Austral. Math. Soc 43 (1) : 153 ~ 159
K. K. Tan / 1993 / Approximating fixed points of nonexpansive mappings by the Ishikawa Iteration process / J. Math. Anal. Appl 178 (2) : 301 ~ 308
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