Strong convergence theorems for nonlinear operator equations with total quasi-ϕ-asymptotically nonexpansive mappings and applications

The purpose of this article is first to introduce the concept of total quasi-ϕ - asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases, and then by using the hybrid algorithm to introduce a new iterative scheme for finding a common element of set of solutions...

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Published inFixed point theory and applications (Hindawi Publishing Corporation) Vol. 2012; no. 1; pp. 1 - 16
Main Authors Wang, Xiong-rui, Chang, Shih-sen, Wang, Lin, Tang, Yong-Kun, Xu, Yu Guang
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.03.2012
BioMed Central Ltd
Subjects
Algorithms
Analysis
Applications of Mathematics
Banach space
Classification
Convergence
Differential Geometry
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Metal oxide semiconductors
Nonlinearity
Topology
asymptotically nonexpansive mappings
Hammerstian type equation
fixed point
quasi
relatively nonexpansive mapping
variational inequalities
total quasi
generalized mixed equilibrium problems
Online AccessGet full text
ISSN1687-1812
1687-1820
1687-1812
DOI10.1186/1687-1812-2012-34

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Abstract The purpose of this article is first to introduce the concept of total quasi-ϕ - asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases, and then by using the hybrid algorithm to introduce a new iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, the set of common fixed points of a countable family of total quasi- ϕ -asymptotically nonexpansive mappings and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. As an application, we shall utilize our results to study the iterative solutions of the nonlinear Hammerstian type equation. The results presented in the article improve and extend the corresponding results announced by some authors. AMS (MOS) subject classification : 47H06; 47H09; 47J05; 47J25.
AbstractList The purpose of this article is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases, and then by using the hybrid algorithm to introduce a new iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, the set of common fixed points of a countable family of total quasi-ϕ-asymptotically nonexpansive mappings and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. As an application, we shall utilize our results to study the iterative solutions of the nonlinear Hammerstian type equation. The results presented in the article improve and extend the corresponding results announced by some authors.AMS (MOS) subject classification: 47H06; 47H09; 47J05; 47J25.
The purpose of this article is first to introduce the concept of total quasi-ϕ - asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases, and then by using the hybrid algorithm to introduce a new iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, the set of common fixed points of a countable family of total quasi- ϕ -asymptotically nonexpansive mappings and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. As an application, we shall utilize our results to study the iterative solutions of the nonlinear Hammerstian type equation. The results presented in the article improve and extend the corresponding results announced by some authors. AMS (MOS) subject classification : 47H06; 47H09; 47J05; 47J25.
The purpose of this article is first to introduce the concept of total quasi--asymptotically nonexpansive mapping which contains many kinds of mappings as its special cases, and then by using the hybrid algorithm to introduce a new iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, the set of common fixed points of a countable family of total quasi--asymptotically nonexpansive mappings and null spaces of finite family of gamma -inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach space. As an application, we shall utilize our results to study the iterative solutions of the nonlinear Hammerstian type equation. The results presented in the article improve and extend the corresponding results announced by some authors. AMS (MOS) subject classification: 47H06; 47H09; 47J05; 47J25.
ArticleNumber 34
Author Wang, Xiong-rui
Wang, Lin
Chang, Shih-sen
Tang, Yong-Kun
Xu, Yu Guang
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crossref_primary_10_1007_s11784_016_0389_6
crossref_primary_10_4236_am_2014_51004
crossref_primary_10_1007_s11784_019_0690_2
Cites_doi 10.1016/0362-546X(91)90200-K
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Copyright_xml – notice: Wang et al.; licensee Springer. 2012. This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License ( ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Issue 1
Keywords asymptotically nonexpansive mappings
Hammerstian type equation
fixed point
quasi
relatively nonexpansive mapping
variational inequalities
total quasi
generalized mixed equilibrium problems
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  ident: 128_CR11
  publication-title: Nonlinear Anal Hybrid Syst
  doi: 10.1016/j.nahs.2008.10.002
– start-page: 15
  volume-title: Theory and Applications of Nonlinear Operators of Accretive and Monotone Type
  year: 1996
  ident: 128_CR6
– volume: 13
  start-page: 938
  year: 2002
  ident: 128_CR18
  publication-title: SIAM J Optim
  doi: 10.1137/S105262340139611X
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Snippet The purpose of this article is first to introduce the concept of total quasi-ϕ - asymptotically nonexpansive mapping which contains many kinds of mappings as...
The purpose of this article is first to introduce the concept of total quasi--asymptotically nonexpansive mapping which contains many kinds of mappings as its...
The purpose of this article is first to introduce the concept of total quasi-ϕ-asymptotically nonexpansive mapping which contains many kinds of mappings as its...
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SubjectTerms Algorithms
Analysis
Applications of Mathematics
Banach space
Classification
Convergence
Differential Geometry
Mapping
Mathematical analysis
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Metal oxide semiconductors
Nonlinearity
Topology
Title Strong convergence theorems for nonlinear operator equations with total quasi-ϕ-asymptotically nonexpansive mappings and applications
URI https://link.springer.com/article/10.1186/1687-1812-2012-34
https://www.proquest.com/docview/1439731726
http://dx.doi.org/10.1186/1687-1812-2012-34
Volume 2012
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