CAT(0) 空间中可数族拟-非扩张映射的分裂公共不动点问题

数学物理学报 ›› 2026, Vol. 46 ›› Issue (6): 2093-2105.

CAT(0) 空间中可数族拟-非扩张映射的分裂公共不动点问题

高冬雪(), 严亮(), 邓伟奇^*()

云南财经大学统计与数学学院昆明 650221

收稿日期:2025-03-27 修回日期:2025-06-11 出版日期:2026-12-26 发布日期:2026-08-14
通讯作者: 邓伟奇 E-mail:gl349884543@163.com;yl960317@sina.com;dwq1273@126.com
作者简介:高冬雪,E-mail: gl349884543@163.com;
严亮,E-mail: yl960317@sina.com
基金资助:
国家自然科学基金(11223344)

The Split Common Fixed Point Problem for Countable Families of Quasi-Nonexpansive Mappings in CAT(0) Spaces

Dongxue Gao(), Liang Yan(), Weiqi Deng^*()

School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming 650221

Received:2025-03-27 Revised:2025-06-11 Online:2026-12-26 Published:2026-08-14
Contact: Weiqi Deng E-mail:gl349884543@163.com;yl960317@sina.com;dwq1273@126.com
Supported by:
NSFC(11223344)

摘要/Abstract

摘要：

该文研究了 CAT(0) 空间中可数族拟—非扩张映射的分裂公共不动点问题. 为求解该问题, 构造了一种 Mann 型迭代算法, 并在适当的条件下, 证明了该迭代序列的弱收敛性. 相比已有方法, 所提出的算法在更一般的空间结构下构造迭代过程, 从而推广了分裂公共不动点问题的适用范围, 并改进了相关理论结果.

关键词: CAT(0) 空间, 分裂公共不动点问题, 拟-非扩张映射, 可数族.

Abstract:

This paper studies the split common fixed point problem for countable families of quasi-nonexpansive mappings in a CAT(0) space. To solve this problem, a Mann-type iterative algorithm is proposed, and the weakly convergence of the generated sequence is established under appropriate conditions. Compared with existing methods, the proposed algorithm constructs the iterative process in a more general space setting, thereby extending the applicability of the split common fixed point problem and improving related theoretical results.

Key words: CAT(0) space, split common fixed point problem, quasi-nonexpansive mapping, countable family.

中图分类号:

O175.23

高冬雪, 严亮, 邓伟奇. CAT(0) 空间中可数族拟-非扩张映射的分裂公共不动点问题[J]. 数学物理学报, 2026, 46(6): 2093-2105.

Dongxue Gao, Liang Yan, Weiqi Deng. The Split Common Fixed Point Problem for Countable Families of Quasi-Nonexpansive Mappings in CAT(0) Spaces[J]. Acta mathematica scientia,Series A, 2026, 46(6): 2093-2105.

参考文献 22

[1]	Censor Y, Elfving T. A multiprojection algorithm using Bregman projections in a product space. Numerical Algorithms, 1994, 8(2): 221-239 doi: 10.1007/BF02142692
[2]	Censor Y, Segal A. The split common fixed point problem for directed operators. Journal of Convex Analysis, 2009, 16(2): 587-600
[3]	Moudafi A. The split common fixed-point problem for demicontractive mappings. Inverse Problems, 2010, 26(5): Art 055007
[4]	Moudafi A. Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear Convex Analysis, 2014, 15(4): 809-818
[5]	Deng W Q. The split common fixed point problem for infinite families of total quasi-asymptotically nonexpansive operators. Numerical Algorithms, 2014, 67(2): 243-256 doi: 10.1007/s11075-013-9785-9
[6]	Taiwo A, Jolaoso L O, Mewomo O T. Inertial-type algorithm for solving split common fixed point problems in Banach spaces. Journal of Scientific Computing, 2021, 86: Art 12
[7]	Chang S S, Wang L, Tang Y K, et al. The split common fixed point problem for total asymptotically strictly pseudocontractive mappings. Journal of Applied Mathematics, 2012, 2012(1): 385638 doi: 10.1155/jama.v2012.1
[8]	Cui H, Wang F. Iterative methods for the split common fixed point problem in Hilbert spaces. Fixed Point Theory and Applications, 2014, 2014(1): Art 78
[9]	Cui H, Ceng L. Iterative solutions of the split common fixed point problem for strictly pseudo-contractive mappings. Journal of Fixed Point Theory and Applications, 2018, 20: Art 92
[10]	Eslamian M, Eslamian P. Strong convergence of a split common fixed point problem. Numerical Functional Analysis and Optimization, 2016, 37(10): 1248-1266 doi: 10.1080/01630563.2016.1200076
[11]	Qin L J, Wang L, Chang S S. Multiple-set split feasibility problem for a finite family of asymptotically quasi-nonexpansive mappings. Panamerican Mathematical Journal, 2012, 22(1): 37-45
[12]	Xiao J, Wang Y. A viscosity method with inertial effects for split common fixed point problems of demicontractive mappings. Journal of Nonlinear Functional Analysis, 2022, 2022: Art 17
[13]	Godwin E C, Taiwo A, Mewomo O T. Iterative method for solving split common fixed point problem of asymptotically demicontractive mappings in Hilbert spaces. Numerical Algebra, Control and Optimization, 2023, 13(2): 239-257 doi: 10.3934/naco.2022005
[14]	Zhu L J, Yao J C, Yao Y. Approximating solutions of a split fixed point problem of demicontractive operators. Carpathian Journal of Mathematics, 2024, 40(1): 195-206 doi: 10.37193/CJM
[15]	Kirk W A. Malaga/Seville, Geodesic geometry and fixed point theory//Seminar of Mathematical Analysis, September 2002-February 2003, 2002/ 2003: 195-225
[16]	Kirk W A. Geodesic geometry and fixed point theory II. Fixed Point Theory and Applications 2004, 64: 113-142
[17]	Deng W Q, Qian S G. The split common fixed point problem for quasi-nonexpansive mappings in CAT(0) spaces. Journal of Nonlinear and Convex Analysis, 2017, 18(11): 2075-2081
[18]	Abbas M, Ibrahim Y, Khan A R, et al. Split variational inclusion problem and fixed point problem for a class of multivalued mappings in CAT(0) spaces. Mathematics, 2019, 7(8): Art 749
[19]	Rashid M, Kalsoom A, Albargi A H, et al. Convergence result for solving the split fixed point problem with multiple output sets in nonlinear spaces. Mathematics, 2024, 12(12): Art 1825
[20]	Opial Z. Weak convergence of the sequence of successive approximations for nonexpansive mappings. Bulletin of the American Mathematical Society, 1967, 73: 591-597 doi: 10.1090/bull/1967-73-04
[21]	Dhompongsa S, Panyanak B. On $\Delta$-convergence theorems in CAT(0) spaces. Computers & Mathematics with Applications, 2008, 56(10): 2572-2579
[22]	Deng W Q, Bai P. An implicit iteration process for common fixed points of two infinite families of asymptotically nonexpansive mappings in Banach spaces. Journal of Applied Mathematics, 2013, 2013: Art 602582