Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/mann-iteration-of-weak-convergence-theorems-in-banach-space-rOvFufoo8R
References (20)
-
S. Reich (1979)
Weak convergence theorems for nonexpansive mappings in Banach spacesJournal of Mathematical Analysis and Applications, 67
-
M. Osilike, S. Aniagbosor (2000)
Weak and strong convergence theorems for fixed points of asymptotically nonexpensive mappingsMathematical and Computer Modelling, 32
-
D. Dulst (1982)
Equivalent Norms and the Fixed Point Property for Nonexpansive MappingsJournal of The London Mathematical Society-second Series
-
C. Chidume (2005)
THE ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS AN EXAMPLE ON THE MANN ITERATION METHOD FOR LIPSCHITZ PSEUDOCONTRACTIONS -
Zhenyu Huang (2007)
Equivalence theorems of the convergence between Ishikawa and Mann iterations with errors for generalized strongly successively Φ-pseudocontractive mappings without Lipschitzian assumptionsJournal of Mathematical Analysis and Applications, 329
-
Hong-Kun Xu (1991)
Inequalities in Banach spaces with applicationsNonlinear Analysis-theory Methods & Applications, 16
-
Ronald Bruck (1979)
A simple proof of the mean ergodic theorem for nonlinear contractions in Banach spacesIsrael Journal of Mathematics, 32
-
Xianling Fan (2007)
Amemiya Norm Equals Orlicz Norm in Musielak–Orlicz SpacesActa Mathematica Sinica, English Series, 23
-
J. Schu (1991)
Iterative construction of fixed points of asymptotically nonexpansive mappingsJournal of Mathematical Analysis and Applications, 158
-
B. Prus, R. Smarzewski (1987)
Strongly unique best approximations and centers in uniformly convex spacesJournal of Mathematical Analysis and Applications, 121
-
C.E. Chidume, S.A. Mutangadura (2001)
An example on the Mann iteration method for Lipschitz pseudocontractionsProc. Amer. Math. Soc., 129
-
Lianggen Hu (2007)
An Implicit Iteration Process with Errors for a Finite Family of r−strictly Asymptotically Pseudocontractive MappingsActa Mathematicae Applicatae Sinica, English Series, 23
-
A. Rafiq (2007)
On Mann iteration in Hilbert spacesNonlinear Analysis-theory Methods & Applications, 66
-
F., E., Browder, V. W., Petryshyn (1967)
Construction of fixed points of nonlinear mappings in Hilbert spaceJournal of Mathematical Analysis and Applications, 20
-
C.E. Chidume (1987)
Iterative approximation of Lipschitz strictly pseudocontractive mappingsProc. Amer. Math. Soc., 99
-
G. Marino, Hong-Kun Xu (2007)
WEAK AND STRONG CONVERGENCE THEOREMS FOR STRICT PSEUDO-CONTRACTIONS IN HILBERT SPACESJournal of Mathematical Analysis and Applications, 329
-
Z. Opial (1967)
Weak convergence of the sequence of successive approximations for nonexpansive mappingsBulletin of the American Mathematical Society, 73
-
F. Browder (1976)
Nonlinear operators and nonlinear equations of evolution in Banach spaces -
C. Chidume (1987)
Iterative approximation of fixed points of Lipschitzian strictly pseudocontractive mappings, 99
-
F. Browder (1967)
Convergence theorems for sequences of nonlinear operators in Banach spacesMathematische Zeitschrift, 100
- Publisher
- Springer Journals
- Copyright
- Copyright © 2009 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH
- Subject
- Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
- ISSN
- 0168-9673
- eISSN
- 1618-3932
- DOI
- 10.1007/s10255-007-7054-1
- Publisher site
- See Article on Publisher Site
Abstract
In this paper, by using Mann’s iteration process we will establish several weak convergence theorems for approximating a fixed point of k-strictly pseudocontractive mappings with respect to p in p-uniformly convex Banach spaces. Our results answer partially the open question proposed by Marino and Xu, and extend Reich’s theorem from nonexpansive mappings to k-strict pseudocontractive mappings.
Journal
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Mar 17, 2009