Abstract
Under more general form and more general conditions an affirmative answer to Reich's open question is given. The results presented also extend and improve some recent results of Reich, Shioji, Takahashi and Wittmann.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Goebel K, Kirk W A. A fixed point theorem for asymptotically nonexpansive mappings[J].Proc Amer Math Soc,1972,35(1):171–174.
Deimling K.Nonlinear Functional Analysis[M]. Berlin: Springer-Verlag, 1985.
Asplund E. Positivity of duality mappings[J].Bull Amer Math Soc, 1967,73,200–203.
Reich S. Some problems and results in fixed point theory[J].Contem Math,1983,21:179–187.
Reich S. Strong convergence theorems for resolvent of accretive mappings in Banach spaces[J].J Math Anal Appl,1980,75:287–292.
Wittmann R. Approximation of fixed points of nonexpansive mappings[J].Arch Math,1992,58:486–491.
Shioji N, Takahashi W. Strong convergence of approximated sequence for nonexpansive mappings [J].Proc Amer Math Soc,1997,125(12):3641–3645
Takahashi W. On Reich's strong convergence theorems for resolvents of accretive operators[J].J Math Anal Appl,1984,104:546–553.
Chang S S. Some problems and results in the study of nonlinear analysis[J].Nonlinear Anal TMA, 1997,30(7):4197–4208.
Liu L S. Ishikawa and Mann iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces[J].J Math Anal Appl1995,194:114–125.
Author information
Authors and Affiliations
Additional information
Contributed by Zuphang Shi-sheng
Biography: Zuphang Shi-sheng (1934≈)
Rights and permissions
About this article
Cite this article
Shi-sheng, Z. On reich's open question. Appl Math Mech 24, 646–653 (2003). https://doi.org/10.1007/BF02437865
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02437865