Banach空间中关于m-增生算子零点的黏性隐式迭代序列的强收敛定理

潘灵荣 王元恒

摘 要：在自反一致凸Banach空間中，构造了一种关于m-增生算子零点的隐性黏滞迭代序列，在合适的参数条件下，证明了该迭代序列的强收敛定理，所得结论改进和推广了一些相关文献的主要结果。

关键词：Banach空间；m-增生算子；黏性隐式方法；强收敛；变分不等式

中图分类号：O177.91

文献标志码：A

文章编号 1000-5269（2023）03-0011-07

DOI：10.15958/j.cnki.gdxbzrb.2023.03.02

参考文献：

[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 & 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.

（責任编辑：于慧梅）

基金项目：国家自然科学基金资助项目（12171435）

作者简介：潘灵荣（1984—），男，讲师，硕士，研究方向：非线性泛函分析，E-mail：2671825414@qq.com.

*通讯作者：潘灵荣，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