Approximate smoothness in normed linear spaces

被引：2

作者：

Chmielinski, Jacek ^{[1
]}

Khurana, Divya ^{[2
]}

Sain, Debmalya ^{[3
]}

机构：

[1] Pedag Univ Krakow, Dept Math, Podchorazych 2, PL-30084 Krakow, Poland

[2] IIM Ranchi Suchana Bhawan, Humanities & Appl Sci, Audrey House Campus,Meurs Rd, Ranchi 834008, Jharkhand, India

[3] Indian Inst Informat Technol, Dept Math, Raichur 584135, Karnataka, India

来源：

BANACH JOURNAL OF MATHEMATICAL ANALYSIS | 2023年 / 17卷 / 03期

关键词：

Smoothness; Rotundity; Approximate smoothness; Approximate rotundity; Birkhoff-James orthogonality; Approximate Birkhoff-James orthogonality; Supporting hyperplanes; Polyhedral spaces; Direct sums; BIRKHOFF-JAMES ORTHOGONALITY;

D O I：

10.1007/s43037-023-00263-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce the notion of approximate smoothness in a normed linear space. We characterize this property and show the connections between smoothness and approximate smoothness for some spaces. As an application, we consider in particular the Birkhoff-James orthogonality and its right-additivity under the assumption of approximate smoothness.

引用

页数：23

共 50 条

[31] LINEAR NORMED SPACES WITH EXTENSION PROPERTY
ELLIOTT, G
HALPERIN, I
CANADIAN MATHEMATICAL BULLETIN, 1966, 9 (04): : 433 - &
[32] FULLY CONVEX NORMED LINEAR SPACES
FAN, K
GLICKSBERG, I
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1955, 41 (11) : 947 - 953
[33] ON SOME INEQUALITIES IN NORMED LINEAR SPACES
Dragomir, S. S.
TAMKANG JOURNAL OF MATHEMATICS, 2009, 40 (03): : 225 - 237
[34] On Rectangular Constant in Normed Linear Spaces
Paul, Kallol
Ghosh, Puja
Sain, Debmalya
JOURNAL OF CONVEX ANALYSIS, 2017, 24 (03) : 917 - 925
[35] A WEIERSTRASS THEOREM FOR NORMED LINEAR SPACES
PRENTER, PM
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1969, 75 (04) : 860 - &
[36] SCHWARZS LEMMA IN NORMED LINEAR SPACES
HARRIS, LA
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1969, 62 (04) : 1014 - &
[37] Torricellian points in normed linear spaces
Sever S Dragomir
Dan Comǎnescu
Eder Kikianty
Journal of Inequalities and Applications, 2013
[38] On neutrosophic n−normed linear spaces
Kumar V.
Sharma A.
Murtaza S.
Neutrosophic Sets and Systems, 2023, 61 : 275 - 288
[39] Bilinear Operators on Normed Linear Spaces
Nakasho, Kazuhisa
FORMALIZED MATHEMATICS, 2019, 27 (01): : 15 - 23
[40] ON NORMED ALMOST LINEAR-SPACES
GODINI, G
MATHEMATISCHE ANNALEN, 1988, 279 (03) : 449 - 455

← 1 2 3 4 5 →