scholarly journals Hölder’s means and triangles inscribed in a semicircle in Banach spaces

Filomat ◽  
2012 ◽  
Vol 26 (2) ◽  
pp. 371-377
Author(s):  
Huanhuan Cui ◽  
Ge Lu
Keyword(s):  
Banach Spaces ◽  
Geometric Properties ◽  
The Stability ◽  
Geometric Constants

By the H?lder?s means, we introduce two classes geometric constants for Banach spaces. We study some geometric properties related to these constants and the stability under norm perturbations of them.

scholarly journals Some Properties Concerning the JL(X) and YJ(X) Which Related to Some Special Inscribed Triangles of Unit Ball

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1285
Author(s):  
Asif Ahmad ◽  
Yuankang Fu ◽  
Yongjin Li
Keyword(s):  
Unit Ball ◽  
Banach Spaces ◽  
Uniformly Convex ◽  
Geometric Properties ◽  
James Constant ◽  
Von Neumann ◽  
Geometric Constants

In this paper, we will make some further discussions on the JL(X) and YJ(X) which are symmetric and related to the side lengths of some special inscribed triangles of the unit ball, and also introduce two new geometric constants L1(X,▵), L2(X,▵) which related to the perimeters of some special inscribed triangles of the unit ball. Firstly, we discuss the relations among JL(X), YJ(X) and some geometric properties of Banach spaces, including uniformly non-square and uniformly convex. It is worth noting that we point out that uniform non-square spaces can be characterized by the side lengths of some special inscribed triangles of unit ball. Secondly, we establish some inequalities for JL(X), YJ(X) and some significant geometric constants, including the James constant J(X) and the von Neumann-Jordan constant CNJ(X). Finally, we introduce the two new geometric constants L1(X,▵), L2(X,▵), and calculate the bounds of L1(X,▵) and L2(X,▵) as well as the values of L1(X,▵) and L2(X,▵) for two Banach spaces.

scholarly journals On a New Geometric Constant Related to the Euler-Lagrange Type Identity in Banach Spaces

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 116
Author(s):  
Qi Liu ◽  
Yongjin Li
Keyword(s):  
Banach Spaces ◽  
Product Space ◽  
Sufficient Conditions ◽  
Normal Structure ◽  
The Other ◽  
Inner Product ◽  
Equivalent Characterization ◽  
Geometric Constant ◽  
Geometric Constants

In this paper, we will introduce a new geometric constant LYJ(λ,μ,X) based on an equivalent characterization of inner product space, which was proposed by Moslehian and Rassias. We first discuss some equivalent forms of the proposed constant. Next, a characterization of uniformly non-square is given. Moreover, some sufficient conditions which imply weak normal structure are presented. Finally, we obtain some relationship between the other well-known geometric constants and LYJ(λ,μ,X). Also, this new coefficient is computed for X being concrete space.

scholarly journals HUR-approximation of an ELTA functional equation

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4311-4328
Author(s):  
A.R. Sharifi ◽  
Azadi Kenary ◽  
B. Yousefi ◽  
R. Soltani
Keyword(s):  
Functional Equation ◽  
Banach Spaces ◽  
Linear Mapping ◽  
Stability Theorem ◽  
Normed Spaces ◽  
The Stability ◽  
Rassias Stability

The main goal of this paper is study of the Hyers-Ulam-Rassias stability (briefly HUR-approximation) of the following Euler-Lagrange type additive(briefly ELTA) functional equation ?nj=1f (1/2 ?1?i?n,i?j rixi- 1/2 rjxj) + ?ni=1 rif(xi)=nf (1/2 ?ni=1 rixi) where r1,..., rn ? R, ?ni=k rk?0, and ri,rj?0 for some 1? i < j ? n, in fuzzy normed spaces. The concept of HUR-approximation originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-300.

scholarly journals Numerical Reckoning Fixed Points of (ρE)-Type Mappings in Modular Vector Spaces

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 390 ◽  
Author(s):  
Wissam Kassab ◽  
Teodor Ţurcanu
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Iteration Process ◽  
Existence Results ◽  
Data Dependence ◽  
Vector Spaces ◽  
The Stability ◽  
Recent Version

In this paper, we study an iteration process introduced by Thakur et al. for Suzuki mappings in Banach spaces, in the new context of modular vector spaces. We establish existence results for a more recent version of Suzuki generalized non-expansive mappings. The stability and data dependence of the scheme for ρ -contractions is studied as well.

scholarly journals ON THE STABILITY OF THE DIFFERENTIAL PROCESS GENERATED BY COMPLEX INTERPOLATION

2020 ◽  
pp. 1-32
Author(s):  
Jesús M. F. Castillo ◽  
Willian H. G. Corrêa ◽  
Valentin Ferenczi ◽  
Manuel González
Keyword(s):  
Unit Circle ◽  
Banach Spaces ◽  
Local Stability ◽  
Interpolation Method ◽  
Complex Interpolation ◽  
Analytic Family ◽  
Köthe Spaces ◽  
The Stability ◽  
Stability Results ◽  
Differential Process

We study the stability of the differential process of Rochberg and Weiss associated with an analytic family of Banach spaces obtained using the complex interpolation method for families. In the context of Köthe function spaces, we complete earlier results of Kalton (who showed that there is global bounded stability for pairs of Köthe spaces) by showing that there is global (bounded) stability for families of up to three Köthe spaces distributed in arcs on the unit circle while there is no (bounded) stability for families of four or more Köthe spaces. In the context of arbitrary pairs of Banach spaces, we present some local stability results and some global isometric stability results.

scholarly journals On the stability of radical septic functional equations

Mathematics ◽  
2020 ◽  
Vol 8 (12) ◽  
pp. 2229
Author(s):  
Emanuel Guariglia ◽  
Kandhasamy Tamilvanan
Keyword(s):  
Functional Equation ◽  
Approximate Solution ◽  
Vector Space ◽  
Banach Spaces ◽  
Functional Equations ◽  
Normed Vector Space ◽  
Relevant Case ◽  
The Stability ◽  
Normed Vector ◽  
Stability Results

This paper deals with the approximate solution of the following functional equation fx7+y77=f(x)+f(y), where f is a mapping from R into a normed vector space. We show stability results of this equation in quasi-β-Banach spaces and (β,p)-Banach spaces. We also prove the nonstability of the previous functional equation in a relevant case.

scholarly journals A note on the stability of nonsurjective $\varepsilon $-isometries of Banach spaces

2020 ◽  
Vol 148 (11) ◽  
pp. 4837-4844
Author(s):  
Lixin Cheng ◽  
Yunbai Dong
Keyword(s):  
Banach Spaces ◽  
The Stability

scholarly journals The () Property in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-7
Author(s):  
Danyal Soybaş
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Banach Spaces ◽  
Bounded Linear Operator ◽  
Isomorphic Copy ◽  
Weakly Compact ◽  
Geometric Properties ◽  
Bounded Linear ◽  
Real Functions

A Banach space is said to have (D) property if every bounded linear operator is weakly compact for every Banach space whose dual does not contain an isomorphic copy of . Studying this property in connection with other geometric properties, we show that every Banach space whose dual has (V∗) property of Pełczyński (and hence every Banach space with (V) property) has (D) property. We show that the space of real functions, which are integrable with respect to a measure with values in a Banach space , has (D) property. We give some other results concerning Banach spaces with (D) property.

Sign in / Sign up

Export Citation Format

Share Document