Journal of Guangxi Normal University(Natural Science Edition) ›› 2024, Vol. 42 ›› Issue (6): 194-204.doi: 10.16088/j.issn.1001-6600.2023111602

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Generalized Viscosity Three-step Implicit Double Midpoint Rule for Non-expansive Mappings

PENG Jianying, GAO Xinghui*, ZHANG Yuting   

  1. School of Mathematics and Computer Science, Yan’an University, Yan’an Shaanxi 716000, China
  • Received:2023-11-16 Revised:2024-01-18 Online:2024-12-30 Published:2024-12-30

Abstract: The iterative algorithm for fixed points is a hot topic in nonlinear functional analysis research. The viscosity algorithm for constructing a new generalized three-step implicit double midpoint rule for non-expanding mappings with fixed points in a uniformly smooth Banach spaces is proposed. Under appropriate conditions, the dual mapping definition and Banach limit definition and techniques are used to prove that the iterative sequence generated by this algorithm strongly converges to the common element of the common fixed point set of three non-expanding mappings, and the inference in special cases is given. The results improve and generalize the relevant results in recent literature.

Key words: Banach spaces, non-expanding mapping, generalized implicit double midpoint rule, strong convergence, fixed points

CLC Number:  O177.91
[1] BADER G, DEUFIHARD P. A semi-implicit mid-point rule for stiff systems of ordinary differential equations[J].Numerische Mathematik, 1983, 41: 373-398.
[2] DEUFLHARD P. Recent progress in extrapolation methods for ordinary differential equations[J]. Society for Industrial and Applied Mathematics, 1985, 27(4): 505-535.
[3] ALGHAMDI M A, ALGHAMDI M ALI, SHAHZAD N, et al. The implicit midpoint rule for non-expansive mappings[J]. Fixed Point Theory and Applications, 2014, 2014:96.
[4] CAI G, SHEHU Y, lYIOLA O S. Modified viscosity implicit rules for nonexpansive mappings in Hilbert spaces[J]. Journal of Fixed Point Theory and Applications, 2017, 19(4): 2831-2846.
[5] XU H K, ALGHAMDI M A, SHAHZAD N. The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces[J]. Fixed Point Theory and Applications, 2015, 2015: 41.
[6] YAO Y H, SHAHZAD N, LIOU Y C. Modified semi-implicit midpoint rule for nonexpansive mappings[J]. Fixed Point Theory and Applications, 2015, 2015: 166.
[7] 蔡钢.Hilbert空间中关于变分不等式问题和不动点问题的粘性隐式中点算法[J].数学物理学报, 2020, 40(2): 395-407.
[8] 于玉,非线性映像的复合粘性中点迭代法与应用于变分不等式系统[D].上海:上海师范大学, 2021.
[9] 贺龙,基于隐式中点的不动点问题与分裂可行性问题的迭代算法研究[D].银川:北方民族大学, 2020.
[10] ZHANG H C, QU Y H, SU Y F. The generalized viscosity implicit midpoint rule for nonexpansive mappings in Banach Space[J]. Mathematics, 2019, 7(6): 512.
[11] DHAKAL S, SINTUNAVARAT W. The viscosity method for the implicit double midpoint rule with numerical results and its applications[J]. Computation and Applied Mathematics, 2019, 38(2): 40.
[12] KE Y F, MA C F. The generalized viscosity implicit rules of nonexpansive mappings in Hilbert spaces[J]. Fixed Point Theoryand Applications. 2015, 2015: 190.
[13] PAN C J, WANG Y H. Generalized viscosity implicit iterative process for asymptotically non-expansive mappings in Banach spaces[J]. Mathematics, 2019, 7(5): 379.
[14] 王元恒,李参参. Banach空间中渐近非扩张映射的广义粘性隐式双中点法则[J]. 数学学报(中文版), 2021, 64(4): 601-612.
[15] 管金林,唐艳. Banach空间中三步隐式中点法则算法的研究及应用[J].数学学报(中文版), 2023, 66(5): 971-980.
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