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Strong convergence results on the common fixed points of asymptotically pseudocontractive semigroups(PDF)

《纺织高校基础科学学报》[ISSN:1006-6977/CN:61-1281/TN]

Issue:
2017年02期
Page:
200-206
Research Field:
Publishing date:

Info

Title:
Strong convergence results on the common fixed points of asymptotically pseudocontractive semigroups
Author(s):
FAN Qinwei1HUI Zhen2HE Huimin3
1.School of Science, Xi’an Polytechnic University, Xi’an 710048, China;
2.Administrative Office of Network and Informatization, Xi’an Polytechnic University, Xi’an 710048, China;
3.School of Mathematics and Statistics, Xidian University, Xi’an 710071, China
Keywords:
 fixed points pseudocontractive semigroups strong convergence Banach space
PACS:
O177.91
DOI:
10.13338/j.issn.1006-8341.2017.02.007
Abstract:
In order to study the strong convergence of asymptotically pseudocontractive semigroups in a real Banach space,a viscosity iteration algorithm for approximating the common fixed point of asymptotically pseudocontractive semigroups is proposed, and it is proved that the common fixed point is also unique solution to a variational inequality. The results mainly extend the results of Ref.[8] from the Halpern iteration algorithm to viscosity iteration algorithm, and also extend the results of Ref.[9] from nonexpansive semigroups to asymptotically pseudocontractive semigroups.

References:

[1] SCHU J.Iterative construction of fixed point of asymptotically nonexpansive mappings[J].J Math Anal Apll,1991,158(2):407-413. [2] GOEBEL K,KIRK W A.A fixed point theorem for asymptotically nonexpansive mappings[J].Proc Amer Math Soc,1972,35(1):171-174. [3] REICH S.Product formulas,nonlinear semigroups and accretive operators[J].J Funct Anal,1980,36(2):147-168. [4] SHIOJI N,TAKAHASHI W.Strong convergence theorems for asymptotically nonexpansive semigroups in Hilbert spaces[J].Nonlinear Anal,1998,34(1):87-99. [5] SUZUKI T.On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces[J].Proc Amer Math Soc,2002,131(7):2133-2136. [6] THUY N T T,HIEU P T,STRODIOT J J.Regularization methods for accretive variational inequalities over the set of common fixed points of nonexpansive semigroups[J].Optimization,2016,65(8):1553-1567. [7] YAO Y H,KANG J I,CHAO Y J,et al.Approximation of fixed points for nonexpansive semigroups in Hilbert spaces[J].Fixed Point Theory and Applications,2013(1):31. [8] CHIDUME C,E.Strong convergence theorems for fixed points of asymptotically pseudocontractive semigroups[J].J Math Anal Apll,2004,296(2):410-421. [9] CHEN R D,HE H M.Viscosity approximation of common fixed points of nonexpansive semigroups in Banach space[J].Appl Math Lett,2007,20(7):751-757. [10] HIEU P T,THUY N T T.Regularization methods for nonexpansive semigroups in Hilbert spaces[J].Vietnam J Math,2016,44(3):1-12. [11] KOZLOWSKI W M.On convergence of iteration processes for nonexpansive semigroups in uniformly convex and uniformly smooth Banach spaces[J].J Math Anal Apll,2015,426(2):1182-1191. [12] BYNUM W L.Normal structure coefficients for Banach spaces[J].Pacific J Math,2001,86(2):427-436. [13] AKSOY A G,KHAMSI M A.Nonstandard methods in fixed point theory[M].New York:Springe-Verlag,1990. [14] TAKAHASHI W.Nonlinear functional analysis[M].Japan:Yokohama Publishers,2000. [15] KATO T.Nonlinear semigroups and evolution equations[J].J Math Soc Japan,1967(19):508-520. [16] LIM T C,XU H K.Fixed point theorems for asymptotically nonexpansive mappings[J].Nonlinear Anal,1994,22(11):1345-1355. [17] REICH S.Iteractive methods for accretive sets[J].Nonlinear Equations in Abstract Spaces,1978:317-326. [18] BARBU V,PRECUPANU T.Convexity and optimization in Banach spaces[M].Editura Academiei,1991,24(3):317. [19] XU H K.Inequalities in Banach spaces with applications[J].Nonlinear Anal,1991,16(12):1127-1138. [20] MORALES C,JUNG J.Convergence of paths for pseudocontractive mappings in Banach spaces[J].Proc Amer Math Soc,2000,128(11):3411-3419.

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Last Update: 2017-07-22