ITERATIVE METHODS FOR OBTAINING AN INFINITE FAMILY OF STRICT PSEUDO-CONTRACTIONS IN BANACH SPACES

ITERATIVE METHODS FOR OBTAINING AN INFINITE FAMILY OF STRICT PSEUDO-CONTRACTIONS IN BANACH SPACES

ITERATIVE METHODS FOR OBTAINING AN INFINITE FAMILY OF STRICT PSEUDO-CONTRACTIONS IN BANACH SPACES

Abstract

References

Metrics

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0

doi:10.1007/s10473-022-0504-2

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (5): 1765-1778.doi: 10.1007/s10473-022-0504-2

• Articles • Previous Articles

Meng WEN^1,2, Haiyang LI¹, Changsong HU³, Jigen PENG⁴

1. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China;
2. School of Science, Xi'an Polytechnic University, Xi'an, 710048, China;
3. Department of Mathematics, Hubei Normal University, Huangshi, 435002, China;
4. School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China

Received:2021-03-30 Revised:2022-04-01 Published:2022-11-02
Contact: Jigen Peng,E-mail:jgpengxjtu@126.com E-mail:jgpengxjtu@126.com
Supported by:
This work was supported by the National Natural Science Foundation of China (12001416, 11771347 and 12031003), the Natural Science Foundations of Shaanxi Province (2021JQ-678).

Abstract: In this paper, we introduce a general hybrid iterative method to find an infinite family of strict pseudo-contractions in a q-uniformly smooth and strictly convex Banach space. Moreover, we show that the sequence defined by the iterative method converges strongly to a common element of the set of fixed points, which is the unique solution of the variational inequality $\left\langle(\lambda \varphi-\nu \mathcal{F}) \tilde{z}, j_q(z-\tilde{z})\right\rangle \leq 0$ , for $z \in \bigcap_{i=1}^{\infty} \Gamma\left(S_i\right)$ . The results introduced in our work extend to some corresponding theorems.

Key words: MKC, iterative algorithm, strict pseudo-contraction, β-Lipschitzian, δ-strongly monotone, Banach spaces

CLC Number:

47H09

Meng WEN, Haiyang LI, Changsong HU, Jigen PENG. ITERATIVE METHODS FOR OBTAINING AN INFINITE FAMILY OF STRICT PSEUDO-CONTRACTIONS IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2022, 42(5): 1765-1778.

Trendmd

[1] Diestel J. Geometry of Banach Spaces: Selected Topics. Lecture Notes in Math 485. Springer-Verlag, 1975
[2] Banach S. Surles operations dans les ensembles abstraits et leur application aux equations integrales. Fund Math, 1922, 3: 133–181
[3] Meir A, Keeler E. A theorem on contraction mappings. J Math Anal Appl, 1969, 28: 326–329
[4] Jung J S. Strong convergence of iterative methods for k-strictly pseudo-contractive mappings in Hilbert spaces. Appl Math Comput, 2010, 215: 3746–3753
[5] Tian M. A general iterative algorithm for nonexpansive mappings in Hilbert spaces. Nonlinear Anal, 2010, 73: 689–694
[6] Wang S. A general iterative method for obtaining an infinite family of strictly pseudo-contractive mappings in Hilbert spaces. Appl Math Lett, 2011, 24: 901–907
[7] Cai G, Hu C S. Strong convergence theorems of a general iterative process for a finite family of λ_i-strict pseudo-contractions in q-uniformly smooth Banach spaces. Comput Math Appl, 2010, 59(1): 149–160
[8] Suzuki T. Moudafi’s viscosity approximations with Meir-Keeler contractions. J Math Anal Appl, 2007, 325(1): 342–352
[9] Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bull Amer Math Soc, 1967, 73: 591–597
[10] Gossez J P, Dozo E L. Some geometric properties related to the fixed point theory for nonexpansive mappings. Pacific J Math, 1972, 40: 565–573
[11] Jung J S. Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces. J Math Anal Appl, 2005, 302(2): 509–520
[12] Wen M, Hu CS, Cui AG, et al. Convergence of an explicit scheme for nonexpansive semigroups in Banach spaces. J Fixed Point Theory Appl, 2019, 21: 52
[13] Suzuki T. Strong convergence of Krasnoselskii and Mann’s type sequences for one parameter nonexpansive semigroups without Bochner integral. J Math Anal Appl, 2005, 35: 227–239
[14] Liu L S. Iterative processes with errors for nonlinear strongly accretive mappings in Banach spaces. J Math Anal Appl, 1995, 194: 114–125
[15] Xu H K. Iterative algorithms for nonlinear operators. J London Math Sov, 2002, 66: 240–256
[16] Zhang H, Su Y. Strong convergence theorems for strict pseudo-contractions in q-uniformly smooth Banach spaces. Nonlinear Anal, 2009, 70(9): 3236–3242
[17] Shimoji K, Takahashi W. Strong convergence to common fixed points of infinite nonexpansive mappings and applications. Taiwanese J Math, 2001, 5(2): 387–404
[18] Chang S S. A new method for solving equilibrium problem and variational inequality problem with application to optimization. Nonlinear Anal, 2009, 70: 3307–3319
[19] Song Y L. Strong convergence theorems of a new general iterative process with Meir-Keeler contractions for a countable family of λ_i-strict pseudocontractions in q-uniformly smooth Banach spaces. Fixed Point Theory App, 2010, 19: 354202
[20] Gu F. Convergence of implicit iterative process with errors for a finite family of asymptotically non-expansive mappings. Acta Math Sci, 2006, 26B: 1131–1143

Viewed

Full text

	From	local

	Times	6
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	90

	From	Others

	Times	90
	Rate	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

Just accepted

Online first

Just accepted

Online first

[1]	Ravinder Kumar SHARMA, Sumit CHANDOK. THE GENERALIZED HYPERSTABILITY OF GENERAL LINEAR EQUATION IN QUASI-2-BANACH SPACE [J]. Acta mathematica scientia,Series B, 2022, 42(4): 1357-1372.
[2]	Yuqi SUN, Wen ZHANG. COARSE ISOMETRIES BETWEEN FINITE DIMENSIONAL BANACH SPACES [J]. Acta mathematica scientia,Series B, 2021, 41(5): 1493-1502.
[3]	Zihou ZHANG, Vicente MONTESINOS, Chunyan LIU. SOME METRIC AND TOPOLOGICAL PROPERTIES OF NEARLY STRONGLY AND NEARLY VERY CONVEX SPACES [J]. Acta mathematica scientia,Series B, 2020, 40(2): 369-378.
[4]	Muaadh ALMAHALEBI, Abdellatif CHAHBI. APPROXIMATE SOLUTION OF P-RADICAL FUNCTIONAL EQUATION IN 2-BANACH SPACES [J]. Acta mathematica scientia,Series B, 2019, 39(2): 551-566.
[5]	Lin YU, Ruhui WANG, Shoujiang ZHAO. CARLESON MEASURES AND THE GENERALIZED CAMPANATO SPACES OF VECTOR-VALUED MARTINGALES [J]. Acta mathematica scientia,Series B, 2018, 38(6): 1779-1788.
[6]	Shisheng ZHANG, Lin WANG, Lijuan QIN, Zhaoli MA. STRONGLY CONVERGENT ITERATIVE METHODS FOR SPLIT EQUALITY VARIATIONAL INCLUSION PROBLEMS IN BANACH SPACES [J]. Acta mathematica scientia,Series B, 2016, 36(6): 1641-1650.
[7]	Jing ZHAO, Shengnan WANG. VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS [J]. Acta mathematica scientia,Series B, 2016, 36(5): 1474-1486.
[8]	Eric U. OFOEDU, Charles E. ONYI. APPROXIMATION OF COMMON FIXED POINT OF FAMILIES OF NONLINEAR MAPPINGS WITH APPLICATIONS [J]. Acta mathematica scientia,Series B, 2015, 35(5): 1225-1240.
[9]	Yekini SHEHU. CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING [J]. Acta mathematica scientia,Series B, 2014, 34(4): 1081-1097.
[10]	Yekini SHEHU. APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN#br# BANACH SPACES [J]. Acta mathematica scientia,Series B, 2014, 34(2): 409-423.
[11]	Boulbeba Abdelmoumen, Aref Jeribi, Maher Mnif. ON GRAPH MEASURES IN BANACH SPACES AND DESCRIPTION OF ESSENTIAL SPECTRA OF MULTIDIMENSIONAL TRANSPORT EQUATION [J]. Acta mathematica scientia,Series B, 2012, 32(5): 2050-2064.
[12]	DING Xie-Ping. A NEW CLASS OF BILEVEL GENERALIZED MIXED EQUILIBRIUM PROBLEMS IN BANACH SPACES [J]. Acta mathematica scientia,Series B, 2012, 32(4): 1571-1583.
[13]	H. O. Fattorini. TIME AND NORM OPTIMAL CONTROLS: A SURVEY OF RECENT RESULTS AND OPEN PROBLEMS [J]. Acta mathematica scientia,Series B, 2011, 31(6): 2203-2218.
[14]	GU Feng. NECESSARY AND SUFFICIENT CONDITION OF THE STRONG CONVERGENCE FOR TWO FINITE FAMILIES OF UNIFORMLY#br# L-LIPSCHITZIAN MAPPINGS [J]. Acta mathematica scientia,Series B, 2011, 31(5): 2058-2066.
[15]	Veli Shakhmurov. ABSTRACT CAPACITY OF REGIONS AND COMPACT EMBEDDING WITH APPLICATIONS [J]. Acta mathematica scientia,Series B, 2011, 31(1): 49-67.