Banach空間中關(guān)于m-增生算子零點(diǎn)的黏性隱式迭代序列的強(qiáng)收斂定理

摘 要：在自反一致凸Banach空間中，構(gòu)造了一種關(guān)于m-增生算子零點(diǎn)的隱性黏滯迭代序列，在合適的參數(shù)條件下，證明了該迭代序列的強(qiáng)收斂定理，所得結(jié)論改進(jìn)和推廣了一些相關(guān)文獻(xiàn)的主要結(jié)果。

關(guān)鍵詞：Banach空間；m-增生算子；黏性隱式方法；強(qiáng)收斂；變分不等式

中圖分類號：O177.91

文獻(xiàn)標(biāo)志碼：A

文章編號 1000-5269（2023）03-0011-07

DOI：10.15958/j.cnki.gdxbzrb.2023.03.02

參考文獻(xiàn)：

[1]CENG L C， PETRUEL A， YAO J C， et al. Hybrid viscosity extragradient method for systems of variational inequalities， fixed points of nonexpansive mappings， zero points of accretive operators in Banach spaces［J］. Fixed Point Theory， 2018， 19（2）： 487-502.

［2］ SOW T. Iterative algorithm for computing fixed points of demicontractive and zeros points of multivalued accretive operators in certain Banach spaces with application［J］. Advances in the Theory of Nonlinear Analysis and its Application， 2020， 4（2）： 100-111.

［3］ EJIKEME C L， ABBAS M， AGBEBAKU D F. Convergence results for fixed point problems of accretive operators in banach spaces［J］. Journal of Mathematics and Statistics， 2020， 16（1）： 161-169.

［4］ SONG Y L， PEI Y G. A new viscosity semi-implicit midpoint rule for strict pseudo-contractions and （α，β）-generalized hybrid mappings［J］. Optimization， 2021， 70（12）： 1-19.

［5］ VAISH R， AHMAD M K. Generalized viscosity implicit scheme with Meir-Keeler contraction for asymptotically nonexpansive mapping in Banach spaces［J］. Numerical Algorithms， 2020， 84（3）： 1217-1237.

［6］ XIONG T J， LAN H Y. New two types of semi-implicit viscosity iterations for approximating the fixed points of nonexpansive operators associated with contraction operators and applications［J］. Journal of Inequalities and Applications， 2020， 145： 1-18.

［7］ PANT R， OKEKE C C， IZUCHUKWU C. Modified viscosity implicit rules for proximal split feasibility and fixed point problems［J］. Journal of Applied Mathematics and Computing， 2020， 64（1）： 355-378.

［8］ CENG L C， SHANG M. Generalized mann viscosity implicit rules for solving systems of variational inequalities with constraints of variational inclusions and fixed point problems［J］. Mathematics， 2019， 7（10）： 1-18.

［9］ DHAKAL S， SINTUNAVARAT W. The viscosity method for the implicit double midpoint rule with numerical results and its applications［J］. Computational amp; Applied Mathematics， 2019， 38（40）： 1-18.

［10］JUNG J S. Strong convergence of an iterative algorithm for accretive operators and nonexpansive mappings［J］. Nonlinear Sci Appl， 2016， 9（5）： 2394-2409.

［11］LI D F. On nonexpansive and accretive operators in Banach spaces［J］. Nonlinear Sci Appl， 2017， 10（7）： 3437-3446.

［12］LUO P， CAI G， SHEHU Y. The viscosity iterative algorithms for the implicit midpoint rule of nonexpansive mappings in uniformly smooth Banach spaces［J］. J Inequal Appl， 2017， 154： 1-12.

［13］ZHANG H C， QU Y H， SU Y F. Strong convergence theorems for fixed point problems for nonexpansive mappings and zero point problems for accretive operators using viscosity implicit midpoint rules in Banach spaces［J］. Mathematics， 2018， 6（11）： 1-19.

［14］BARBU V. Nonlinear semigroups and differential equations in Banach spaces［J］. Editura Academiei Republicii Socialiste Romania， 1976， 2： 1-6.

［15］XU H K. Viscosity approximation methods for nonexpansive mappings［J］. J Math Anal Appl， 2004， 298（1）： 279-291.

［16］QIN X L， CHO S Y， WANG L. Iterative algorithms with error for zero points of m-accretive operators［J］. Fixed Point Theory Appl， 2013， 148： 1-17.

（責(zé)任編輯：于慧梅）

基金項(xiàng)目：國家自然科學(xué)基金資助項(xiàng)目（12171435）

作者簡介：潘靈榮（1984—），男，講師，碩士，研究方向：非線性泛函分析，E-mail：2671825414@qq.com.

*通訊作者：潘靈榮，E-mail：2671825414@qq.com.

Abstract： The purpose of this paper is to introduce viscosity implicit algorithms for the zeros of m-accretive operators in reflexive and uniformly convex Banach spaces. Under certain conditions， strong convergence theorem of the sequence generated by the algorithm is proved and the results obtained in this article extend and improve the main results of the existing research.

Key words： Banach space; m-accretive operator; viscosity implicit algorithms; strong convergence; variational inequality