数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 1765-1778.doi: 10.1007/s10473-022-0504-2

• 论文 • 上一篇    

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

Meng WEN1,2, Haiyang LI1, Changsong HU3, Jigen PENG4   

  1. 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
  • 收稿日期:2021-03-30 修回日期:2022-04-01 发布日期:2022-11-02
  • 通讯作者: Jigen Peng,E-mail:jgpengxjtu@126.com E-mail:jgpengxjtu@126.com
  • 基金资助:
    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).

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

Meng WEN1,2, Haiyang LI1, Changsong HU3, Jigen PENG4   

  1. 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).

摘要: 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.

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

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

中图分类号: 

  • 47H09