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

doi:10.1007/s10473-022-0504-2

Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (5): 1765-1778.doi: 10.1007/s10473-022-0504-2

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

Meng WEN^1,2, Haiyang LI¹, Changsong HU³, Jigen PENG⁴

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).

Abstract

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

CLC Number:

47H09

Meng WEN, Haiyang LI, Changsong HU, Jigen PENG. ITERATIVE METHODS FOR OBTAINING AN INFINITE FAMILY OF STRICT PSEUDO-CONTRACTIONS IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2022, 42(5): 1765-1778.

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

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