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Erschienen in: Journal of Inequalities and Applications 1/2014

Open Access 01.12.2014 | Research

Algorithms with variant anchors for pseudocontractive mappings

verfasst von: Lijin Guo, Shin Min Kang, Chahn Yong Jung

Erschienen in: Journal of Inequalities and Applications | Ausgabe 1/2014

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Abstract

The purpose of this paper is to find the fixed points of pseudocontractive mappings by using the iterative technique. Two algorithms with variant anchors have been introduced. Strong convergence results are given. Especially, we can find the minimum-norm fixed point of pseudocontractive mappings.
MSC:47H05, 47H10, 47H17.

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Literatur
1.
Zurück zum Zitat Ceng LC, Petruşel A, Yao JC: Strong convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudocontractive mappings. Appl. Math. Comput. 2009, 209: 162-176. 10.1016/j.amc.2008.10.062MathSciNetCrossRefMATH Ceng LC, Petruşel A, Yao JC: Strong convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudocontractive mappings. Appl. Math. Comput. 2009, 209: 162-176. 10.1016/j.amc.2008.10.062MathSciNetCrossRefMATH
2.
Zurück zum Zitat Chidume CE, Mutangadura SA: An example on the Mann iteration method for Lipschitz pseudo-contractions. Proc. Am. Math. Soc. 2001, 129: 2359-2363. 10.1090/S0002-9939-01-06009-9MathSciNetCrossRefMATH Chidume CE, Mutangadura SA: An example on the Mann iteration method for Lipschitz pseudo-contractions. Proc. Am. Math. Soc. 2001, 129: 2359-2363. 10.1090/S0002-9939-01-06009-9MathSciNetCrossRefMATH
3.
Zurück zum Zitat Chidume CE, Zegeye H: Approximate fixed point sequences and convergence theorems for Lipschitz pseudo-contractive maps. Proc. Am. Math. Soc. 2004, 132: 831-840. 10.1090/S0002-9939-03-07101-6MathSciNetCrossRefMATH Chidume CE, Zegeye H: Approximate fixed point sequences and convergence theorems for Lipschitz pseudo-contractive maps. Proc. Am. Math. Soc. 2004, 132: 831-840. 10.1090/S0002-9939-03-07101-6MathSciNetCrossRefMATH
4.
Zurück zum Zitat Cho SY, Qin X, Kang SM: Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions. Appl. Math. Lett. 2012, 25: 854-857. 10.1016/j.aml.2011.10.031MathSciNetCrossRefMATH Cho SY, Qin X, Kang SM: Hybrid projection algorithms for treating common fixed points of a family of demicontinuous pseudocontractions. Appl. Math. Lett. 2012, 25: 854-857. 10.1016/j.aml.2011.10.031MathSciNetCrossRefMATH
5.
Zurück zum Zitat Ishikawa S: Fixed points by a new iteration method. Proc. Am. Math. Soc. 1974, 44: 147-150. 10.1090/S0002-9939-1974-0336469-5MathSciNetCrossRefMATH Ishikawa S: Fixed points by a new iteration method. Proc. Am. Math. Soc. 1974, 44: 147-150. 10.1090/S0002-9939-1974-0336469-5MathSciNetCrossRefMATH
6.
Zurück zum Zitat Kang SM, Cho SY, Qin X: Hybrid projection algorithms for approximating fixed points of asymptotically quasi-pseudocontractive mappings. J. Nonlinear Sci. Appl. 2012, 5: 466-474.MathSciNetMATH Kang SM, Cho SY, Qin X: Hybrid projection algorithms for approximating fixed points of asymptotically quasi-pseudocontractive mappings. J. Nonlinear Sci. Appl. 2012, 5: 466-474.MathSciNetMATH
7.
Zurück zum Zitat Kang SM, Rafiq A: On convergence results for Lipschitz pseudocontractive mappings. J. Appl. Math. 2012., 2012: Article ID 902601 10.1155/2012/902601 Kang SM, Rafiq A: On convergence results for Lipschitz pseudocontractive mappings. J. Appl. Math. 2012., 2012: Article ID 902601 10.1155/2012/902601
8.
Zurück zum Zitat Kang SM, Rafiq A, Lee S: Convergence analysis of an iterative scheme for Lipschitzian hemicontractive mappings in Hilbert spaces. J. Inequal. Appl. 2013., 2013: Article ID 132 10.1186/1029-242X-2013-132 Kang SM, Rafiq A, Lee S: Convergence analysis of an iterative scheme for Lipschitzian hemicontractive mappings in Hilbert spaces. J. Inequal. Appl. 2013., 2013: Article ID 132 10.1186/1029-242X-2013-132
9.
Zurück zum Zitat Li XS, Kim JK, Huang NJ: Viscosity approximation of common fixed points for L -Lipschitzian semigroup of pseudocontractive mappings in Banach spaces. J. Inequal. Appl. 2009., 2009: Article ID 936121 10.1155/2009/936121 Li XS, Kim JK, Huang NJ: Viscosity approximation of common fixed points for L -Lipschitzian semigroup of pseudocontractive mappings in Banach spaces. J. Inequal. Appl. 2009., 2009: Article ID 936121 10.1155/2009/936121
10.
11.
Zurück zum Zitat Morales CH, Jung JS: Convergence of paths for pseudocontractive mappings in Banach spaces. Proc. Am. Math. Soc. 2000, 128: 3411-3419. 10.1090/S0002-9939-00-05573-8MathSciNetCrossRefMATH Morales CH, Jung JS: Convergence of paths for pseudocontractive mappings in Banach spaces. Proc. Am. Math. Soc. 2000, 128: 3411-3419. 10.1090/S0002-9939-00-05573-8MathSciNetCrossRefMATH
12.
Zurück zum Zitat Ofoedu EU, Zegeye H: Further investigation on iteration processes for pseudocontractive mappings with application. Nonlinear Anal. 2012, 75: 153-162. 10.1016/j.na.2011.08.015MathSciNetCrossRefMATH Ofoedu EU, Zegeye H: Further investigation on iteration processes for pseudocontractive mappings with application. Nonlinear Anal. 2012, 75: 153-162. 10.1016/j.na.2011.08.015MathSciNetCrossRefMATH
13.
Zurück zum Zitat Qin X, Cho YJ, Kang SM, Zhou H: Convergence theorems of common fixed points for a family of Lipschitz quasi-pseudocontractions. Nonlinear Anal. 2009, 71: 685-690. 10.1016/j.na.2008.10.102MathSciNetCrossRefMATH Qin X, Cho YJ, Kang SM, Zhou H: Convergence theorems of common fixed points for a family of Lipschitz quasi-pseudocontractions. Nonlinear Anal. 2009, 71: 685-690. 10.1016/j.na.2008.10.102MathSciNetCrossRefMATH
14.
Zurück zum Zitat Song YS, Chen R: An approximation method for continuous pseudocontractive mappings. J. Inequal. Appl. 2006., 2006: Article ID 28950 10.1155/JIA/2006/28950 Song YS, Chen R: An approximation method for continuous pseudocontractive mappings. J. Inequal. Appl. 2006., 2006: Article ID 28950 10.1155/JIA/2006/28950
15.
Zurück zum Zitat Udomene A: Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudocontractions in Banach spaces. Nonlinear Anal. 2007, 67: 2403-2414. 10.1016/j.na.2006.09.001MathSciNetCrossRefMATH Udomene A: Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudocontractions in Banach spaces. Nonlinear Anal. 2007, 67: 2403-2414. 10.1016/j.na.2006.09.001MathSciNetCrossRefMATH
16.
Zurück zum Zitat Wen DJ, Chen YA: General iterative method for generalized equilibrium problems and fixed point problems of k -strict pseudo-contractions. Fixed Point Theory Appl. 2012., 2012: Article ID 125 10.1186/1687-1812-2012-125 Wen DJ, Chen YA: General iterative method for generalized equilibrium problems and fixed point problems of k -strict pseudo-contractions. Fixed Point Theory Appl. 2012., 2012: Article ID 125 10.1186/1687-1812-2012-125
17.
Zurück zum Zitat Yao Y, Colao V, Marino G, Xu HK: Implicit and explicit algorithms for minimum-norm fixed points of pseudocontractions in Hilbert spaces. Taiwan. J. Math. 2012, 16: 1489-1506.MathSciNetMATH Yao Y, Colao V, Marino G, Xu HK: Implicit and explicit algorithms for minimum-norm fixed points of pseudocontractions in Hilbert spaces. Taiwan. J. Math. 2012, 16: 1489-1506.MathSciNetMATH
18.
Zurück zum Zitat Yao Y, Liou YC: Strong convergence of an implicit iteration algorithm for a finite family of pseudocontractive mappings. J. Inequal. Appl. 2008., 2008: Article ID 280908 10.1155/2008/280908 Yao Y, Liou YC: Strong convergence of an implicit iteration algorithm for a finite family of pseudocontractive mappings. J. Inequal. Appl. 2008., 2008: Article ID 280908 10.1155/2008/280908
19.
Zurück zum Zitat Yao Y, Liou YC, Chen R: Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces. Nonlinear Anal. 2007, 67: 3311-3317. 10.1016/j.na.2006.10.013MathSciNetCrossRefMATH Yao Y, Liou YC, Chen R: Strong convergence of an iterative algorithm for pseudocontractive mapping in Banach spaces. Nonlinear Anal. 2007, 67: 3311-3317. 10.1016/j.na.2006.10.013MathSciNetCrossRefMATH
20.
Zurück zum Zitat Yao Y, Liou YC, Marino G: A hybrid algorithm for pseudo-contractive mappings. Nonlinear Anal. 2009, 71: 4997-5002. 10.1016/j.na.2009.03.075MathSciNetCrossRefMATH Yao Y, Liou YC, Marino G: A hybrid algorithm for pseudo-contractive mappings. Nonlinear Anal. 2009, 71: 4997-5002. 10.1016/j.na.2009.03.075MathSciNetCrossRefMATH
21.
Zurück zum Zitat Yao Y, Marino G, Xu HK, Liou YC: Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces. J. Inequal. Appl. 2014., 2014: Article ID 206 10.1186/1029-242X-2014-206 Yao Y, Marino G, Xu HK, Liou YC: Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces. J. Inequal. Appl. 2014., 2014: Article ID 206 10.1186/1029-242X-2014-206
22.
Zurück zum Zitat Zegeye H, Shahzad N, Alghamdi MA: Convergence of Ishikawa’s iteration method for pseudocontractive mappings. Nonlinear Anal. 2011, 74: 7304-7311. 10.1016/j.na.2011.07.048MathSciNetCrossRefMATH Zegeye H, Shahzad N, Alghamdi MA: Convergence of Ishikawa’s iteration method for pseudocontractive mappings. Nonlinear Anal. 2011, 74: 7304-7311. 10.1016/j.na.2011.07.048MathSciNetCrossRefMATH
23.
Zurück zum Zitat Zegeye H, Shahzad N, Alghamdi MA: Minimum-norm fixed point of pseudocontractive mappings. Abstr. Appl. Anal. 2012., 2012: Article ID 926017 10.1155/2012/926017 Zegeye H, Shahzad N, Alghamdi MA: Minimum-norm fixed point of pseudocontractive mappings. Abstr. Appl. Anal. 2012., 2012: Article ID 926017 10.1155/2012/926017
24.
Zurück zum Zitat Zhou H: Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces. Nonlinear Anal. 2009, 70: 4039-4046. 10.1016/j.na.2008.08.012MathSciNetCrossRefMATH Zhou H: Strong convergence of an explicit iterative algorithm for continuous pseudo-contractions in Banach spaces. Nonlinear Anal. 2009, 70: 4039-4046. 10.1016/j.na.2008.08.012MathSciNetCrossRefMATH
25.
Zurück zum Zitat Yao Y, Shahzad N: New methods with perturbations for non-expansive mappings in Hilbert spaces. Fixed Point Theory Appl. 2011., 2011: Article ID 79 10.1186/1687-1812-2011-79 Yao Y, Shahzad N: New methods with perturbations for non-expansive mappings in Hilbert spaces. Fixed Point Theory Appl. 2011., 2011: Article ID 79 10.1186/1687-1812-2011-79
26.
Zurück zum Zitat Yu ZT, Lin LJ, Chuang CS: Mathematical programming with multiple sets split monotone variational inclusion constraints. Fixed Point Theory Appl. 2014., 2014: Article ID 20 10.1186/1687-1812-2014-20 Yu ZT, Lin LJ, Chuang CS: Mathematical programming with multiple sets split monotone variational inclusion constraints. Fixed Point Theory Appl. 2014., 2014: Article ID 20 10.1186/1687-1812-2014-20
27.
Metadaten
Titel
Algorithms with variant anchors for pseudocontractive mappings
verfasst von
Lijin Guo
Shin Min Kang
Chahn Yong Jung
Publikationsdatum
01.12.2014
Verlag
Springer International Publishing
Erschienen in
Journal of Inequalities and Applications / Ausgabe 1/2014
Elektronische ISSN: 1029-242X
DOI
https://doi.org/10.1186/1029-242X-2014-386

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