混合型渐近非扩张映射合成隐迭代序列的收敛性定理

Abstract

Abstract:

The purpose of this paper is to study the weak and strong convergence of a new composite implicit iteration scheme to a common fixed point for a finite family of asmptotically nonexpansive self-mappings and a finite family of asymptotically nonexpansive nonself-mappings in Banach spaces. The results showed in this paper extend and improve the corresponding results of several authors.

Key words: Mixed type asymptotically nonexpansive mapping, Composite implied iterative scheme, Strong and weak convergence, Common fixed point, Uniformly convex Banach space

CLC Number:

O177.91

Liu Yongquan, Guo Weiping. Convergence Theorems of Composite Implied Iterative Scheme for Mixed Type Asymptotically Nonexpansive Mappings[J].Acta mathematica scientia,Series A, 2015, 35(2): 422-440.

Trendmd

References

[1] Goebel K, Kirk W A. A fixed point theorem for asymptotically nonexpansive mapping. Pro Amer Math Soc, 1972, 35: 171-174

[2] Xu H K, Ori M G. An implicit iterative process for nonexpansive mappings. Numer Funct Anal Optimiz, 2001, 22: 767-773

[3] Sun Z H. Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings. J Math Anal Appl, 2003, 286: 351-358

[4] Thakur B S. Weak and strong convergence of composite implicit iteration process. Appl Math Comput, 2007, 190: 965-973

[5] Gu F. Implicit iterative process for common fixed point of a finite family of asymptotically nonexpansive. Sci Math Hung, 2008, 45(2): 235-250

[6] Chang S S, Tan K K, Lee H W J, Chan C K. On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings. J Math Anal Appl, 2006, 313: 273-283

[7] Guo W, Cho Y J. On the strong convergence of the implicit iterative processes with errors for a finite family of asymptotically nonexpansive mappings. Appl Math Lett, 2008, 21: 1046-1052

[8] Chidume C E, Shahzad N. Strong convergence of an implicit iteration for a finite family of nonexpansive mappings. Nonlinear Anal, 2005, 62: 1149-1156

[9] Gu F. New implicit iterative process with errors for a finite family of nonexpansive mappings. Nonlinear Funct Anal Appl, 2008, 13: 865-875

[10] Gu F. Strong and weak convergence of implicit iterative process with errors for asymptotically nonexpansive mappings. J Appl Anal, 2006, 12: 267-282

[11] Gu F. A new composite implicit iterative process with errors for a finite family nonexpansive mappings in Banach space. Fixed Point Theory Appl, 2006, 2006: 1-11

[12] Liu J A. Some convergence theorems of implicit iterative process for nonexpansive mappings in Banach spaces. Math Commum, 2002, 7: 113-118

[13] Cianciaruso F, Marino G, Wang X. Weak and strong convergence of the Ishikawa iterative process for a finite family of asymptotically nonexpansive mapiings. Appl Math Compt, 2010, 216: 3558-3567

[14] Chidume C E, Ofoedu E U, Zegeye H. Strong and weak convergence theorems for asymptotically nonexpansive mappings. J Math Anal Appl, 2003, 280: 364-374

[15] Wang L. Strong and weak convergence theorems for common fixed points of nonself asymptotically nonexpansive mappings. J Math Anal Appl, 2006, 323: 550-557

[16] Guo W, Guo W. Weak convergence theorems for asymptotically nonself-mappings. Appl Math Lett, 2011, 24: 2181-2185

[17] Wang L. Explicit iteration method for common fixed points of a finite family of nonself asymptotically nonexpansive mappings. Compt Math Appl, 2007, 53: 1012-1019

[18] Guo W, Cho Y J, Guo W. Convergence theorems for mixed type asymptotically nonexpansive mappings. Fixed Point Theory and Applications, 2012, DOI: 10.1186/1687-1812-2012-224

[19] Opial Z. Weak convergence of successive approximations for nonexpansive mappins. Bull Amer Math Soc, 1967, 73: 591-597

[20] Osilike M O, Udomene A. Demiclosedness principle and convergence theorems for strictly pseudocontractive mappings of Browder-Petryshyn type. J Math Anal Appl, 2001, 256: 431-445

[21] Goebel K, Kirk W A. Topic in Metric Fixed Point Theory. Cambridge: Cambridge University Press, 1990

[22] Xu H K. Inequalities in Banach spaces with applications. Nonlinear Anal, 1991, 16: 1127-1138

[23] Falset J G, Kaczor W, Kuczumow T, Reich S. Weak convergence theorems for asymptotically nonexpansive mappings and semigroups. Nonlinear Anal, 2001, 43: 377-401

Convergence Theorems of Composite Implied Iterative Scheme for Mixed Type Asymptotically Nonexpansive Mappings

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Song Jiping, Wang Maofa. Common Fixed Point Results for Generalized Weak Contractions with a Rational Expression in Ordered Partial Metric Spaces [J]. Acta mathematica scientia,Series A, 2017, 37(3): 401-415.
[2]	Deng Weiqi. A System of Split Equilibrium Problems for Sequences of Bifunctions [J]. Acta mathematica scientia,Series A, 2016, 36(4): 763-770.
[3]	Liu Yuanxing, Zhou Haiyun, Wang Peiyuan, Zhou Yu. Three Kinds of Iterative Algorithms for Solving the Constrained Split Common Fixed Point Problem in Hilbert Spaces [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1115-1126.
[4]	PIAO Yong-Jie, JIN Hai-Lan, JIN Yuan-Feng. Unique Common Fixed Points for Four Mappings on \|TVS-Valued Cone Metric Spaces [J]. Acta mathematica scientia,Series A, 2015, 35(1): 172-181.
[5]	XIAO Jian-Zhong, YAN Jie, ZHU Xing-Hua. Explicit, Implicit and Viscosity Iterations for Nonexpansive Cosine Families in Hilbert Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1518-1531.
[6]	YAN Jin-Shi, PIAO Yong-Jie. Common Fixed Points for a Pare of Mappings Satisfying Contractive Conditions with Variable Coefficients \|on Metric Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(3): 700-707.
[7]	WANG Yun-Jie. Existence and Uniqueness of \|Common Fixed Point for Four Mappings on Partial Metric Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(1): 62-69.
[8]	PIAO Yong-Jie. Uniqueness of \|Common Fixed Points for a Family of Maps with \boldmath Φ_j^-Quasi-Contractive Type in 2-Metric Spaces [J]. Acta mathematica scientia,Series A, 2012, 32(6): 1079-1085.
[9]	RAO Ruo-Feng. Iterative Approximation to Common \|Fixed Points of An Infinite Family of Non-self Non-expansive Maps and Strong Convergence of Cesàro Mean Iterations [J]. Acta mathematica scientia,Series A, 2010, 30(6): 1666-1676.
[10]	ZHAO Liang-Cai, ZHANG Shi-Sheng. Viscosity Approximation Methods for Common Fixed Points of Infinite Nonexpansive Nonself-mappings [J]. Acta mathematica scientia,Series A, 2010, 30(4): 1144-1157.
[11]	YANG Li-Ping, XIE Xiang-Sheng. Strong Convergence of Implicit Iterative Scheme with Errors for Nonlinear Mappings [J]. Acta mathematica scientia,Series A, 2010, 30(4): 1062-1070.
[12]	PIAO Yong-Jie. Unique Common Fixed Point \|for a Family of Quasi-contractive Type Maps in Metrically Convex Spaces [J]. Acta mathematica scientia,Series A, 2010, 30(2): 487-493.
[13]	RAO Ro-Feng. New Composite Implicit Iterative Scheme With Errors [J]. Acta mathematica scientia,Series A, 2009, 29(3): 823-831.
[14]	Yang Liping. Strong Convergence of Implicit Iterative Sequence with Errors for a Finite Family of Strictly Pseudocontractive Mappings [J]. Acta mathematica scientia,Series A, 2009, 29(1): 186-192.
[15]	Gu Feng. CONVERGENCE OF IMPLICIT ITERATIVE PROCESS WITH ERRORS FOR A FINITE FAMILY OF ASYMPTOTICALLY NONEXPANSIVE MAPPINGS [J]. Acta mathematica scientia,Series A, 2006, 26(6): 1131-.