CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES

doi:10.1007/s10473-022-0324-4

数学物理学报 ›› 2022, Vol. 42 ›› Issue (3): 1225-1237.doi: 10.1007/s10473-022-0324-4

CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES

商绍强

College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, China

收稿日期:2021-01-13 修回日期:2021-06-28 出版日期:2022-06-26 发布日期:2022-06-24
通讯作者: Shaoqiang SHANG,E-mail:sqshang@163.com E-mail:sqshang@163.com
基金资助:
This research was supported by the "China Natural Science Fund under grant 11871181" and the "China Natural Science Fund under grant 11561053".

CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES

Shaoqiang SHANG

College of Mathematical Sciences, Harbin Engineering University, Harbin, 150001, China

Received:2021-01-13 Revised:2021-06-28 Online:2022-06-26 Published:2022-06-24
Contact: Shaoqiang SHANG,E-mail:sqshang@163.com E-mail:sqshang@163.com
Supported by:
This research was supported by the "China Natural Science Fund under grant 11871181" and the "China Natural Science Fund under grant 11561053".

摘要/Abstract

摘要： In this paper, we prove that if $X$ is an almost convex and 2-strictly convex space, linear operator $T: X \to Y$ is bounded, $N(T)$ is an approximative compact Chebyshev subspace of $X$ and $R(T)$ is a 3-Chebyshev hyperplane, then there exists a homogeneous selection ${T^\sigma }$ of ${T^\partial }$ such that continuous points of ${T^\sigma }$ and ${T^\partial }$ are dense on $Y$.

关键词: Continuous selection, 3-Chebyshev hyperplane, set-valued metric generalized inverses, 2-strictly convex space

Abstract: In this paper, we prove that if $X$ is an almost convex and 2-strictly convex space, linear operator $T: X \to Y$ is bounded, $N(T)$ is an approximative compact Chebyshev subspace of $X$ and $R(T)$ is a 3-Chebyshev hyperplane, then there exists a homogeneous selection ${T^\sigma }$ of ${T^\partial }$ such that continuous points of ${T^\sigma }$ and ${T^\partial }$ are dense on $Y$.

Key words: Continuous selection, 3-Chebyshev hyperplane, set-valued metric generalized inverses, 2-strictly convex space

中图分类号:

46B20

商绍强. CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES[J]. 数学物理学报, 2022, 42(3): 1225-1237.

Shaoqiang SHANG. CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES[J]. Acta mathematica scientia,Series A, 2022, 42(3): 1225-1237.

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CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES

CONTINUOUS SELECTIONS OF THE SET-VALUED METRIC GENERALIZED INVERSE IN 2-STRICTLY CONVEX BANACH SPACES

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