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Chang, Shih-sen,Kim, Jong Kyu,Lee, H. W. Joseph,Chan, Chi Kin Hindawi Publishing Corporation 2011 Fixed point theory and applications Vol.2011 No.1
<P>The purpose of this paper is to study the weak and strong convergence theorems of the implicit iteration process for a countable family of Lipschitzian pseudocontraction mappings in Banach spaces. The results presented in this paper extend and improve some recent results announced by some authors.</P>
Shih-sen Chang,H.W. Joseph Lee,Chi Kin Chan 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
In this paper we present an iterative scheme for finding a com- mon element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscos- ity approximationmethods and under suitable conditions, some strong con- vergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others. In this paper we present an iterative scheme for finding a com- mon element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscos- ity approximationmethods and under suitable conditions, some strong con- vergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.
Chang, Shih-Sen,Lee, H.W. Joseph,Chan, Chi Kin The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1
In this paper we present an iterative scheme for finding a common element of the set of zero points of accretive mappings and the set of fixed points of nonexpansive mappings in Banach spaces. By using viscosity approximation methods and under suitable conditions, some strong convergence theorems for approximating to this common elements are proved. The results presented in the paper improve and extend the corresponding results of Kim and Xu [Nonlinear Anal. TMA 61 (2005), 51-60], Xu [J. Math. Anal. Appl., 314 (2006), 631-643] and some others.
On the Strong Convergence Theorems for Asymptotically Nonexpansive Semigroups in Banach Spaces
Shih-sen Chang,Liang Cai Zhao,Ding Ping Wu 한국전산응용수학회 2009 Journal of applied mathematics & informatics Vol.27 No.1
Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are estab- lished. The results presented in this paper extend and improve some re- cent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133–2136; H. K. Xu. A strong convergence theoremfor contrac- tion semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371– 379; N. Shioji and W. Takahashi. Strong convergence theorems for con- tinuous semigroups in Banach spaces, Math. Japonica. 1(1999)57–66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansivemappings, J. Math. Anal. Appl. 211(1997)71–83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptot- ically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87–99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157–163.] Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are estab- lished. The results presented in this paper extend and improve some re- cent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133–2136; H. K. Xu. A strong convergence theoremfor contrac- tion semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371– 379; N. Shioji and W. Takahashi. Strong convergence theorems for con- tinuous semigroups in Banach spaces, Math. Japonica. 1(1999)57–66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansivemappings, J. Math. Anal. Appl. 211(1997)71–83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptot- ically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87–99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157–163.]
ON THE STRONG CONVERGENCE THEOREMS FOR ASYMPTOTICALLY NONEXPANSIVE SEMIGROUPS IN BANACH SPACES
Chang, Shih-Sen,Zhao, Liang Cai,Wu, Ding Ping The Korean Society for Computational and Applied M 2009 Journal of applied mathematics & informatics Vol.27 No.1
Some strong convergence theorems of explicit iteration scheme for asymptotically nonexpansive semi-groups in Banach spaces are established. The results presented in this paper extend and improve some recent results in [T. Suzuki. On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces, Proc. Amer. Math. Soc. 131(2002)2133-2136; H. K. Xu. A strong convergence theorem for contraction semigroups in Banach spaces, Bull. Aust. Math. Soc. 72(2005)371-379; N. Shioji and W. Takahashi. Strong convergence theorems for continuous semigroups in Banach spaces, Math. Japonica. 1(1999)57-66; T. Shimizu and W. Takahashi. Strong convergence to common fixed points of families of nonexpansive mappings, J. Math. Anal. Appl. 211(1997)71-83; N. Shioji and W. Takahashi. Strong convergence theorems for asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. TMA, 34(1998)87-99; H. K. Xu. Approximations to fixed points of contraction semigroups in Hilbert space, Numer. Funct. Anal. Optim. 19(1998), 157-163.]
Chang, Shih-Sen,Cho, Yeol-Je,Kim, Jong-Kyu Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.4
Some convergence theorems for approximating to a common fixed point of an infinite family of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in the setting of Banach spaces by using a new composite implicit iterative process with errors. The results presented in the paper generalize and improve the main results of Bai and Kim [1], Gu [4], Osilike [5], Su and Li [7], and Xu and Ori [8].
APPROXIMATIONS OF THE ITERATIVE SEQUENCES FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES
Chang, Shih-Sen,Cho, Yeol-Je,Zhou, Haiyun The Youngnam Mathematical Society Korea 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we first introduce some iterative sequences of Halpern type for asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces and then we discuss strong convergence for the iterative processes. The results presented in this paper extend, supplement and improve the correspoding main results of Reich [11], Shimizu and Takahashi [13], Shioji and Takahashi [15], [16] and Wittmann [18].
APPROXIMATIONS OF THE ITERATIVE SEQUENCES FOR ASYMPTOTICALLY NONEXPANSIVE MAPPINGS IN BANACH SPACES
조열제,Shih-Sen Chang,Haiyun Zhou 영남수학회 2008 East Asian mathematical journal Vol.24 No.1
In this paper, we first introduce some iterative sequences of Halpern type for asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces and then we discuss strong convergence for the iterative processes. The results presented in this paper extend, supplement and improve the correspoding main results of Reich [11], Shimizu and Takahashi [13], Shioji and Takahashi [15], [16] and Wittmann [18].