On completeness of the space of weighted Stepanov-like pseudo almost automorphic (periodic) functions

被引：4

作者：

He, Bing ^{[1
,2
]}

Wang, Qi-Ru ^{[1
]}

机构：

[1] Sun Yat Sen Univ, Sch Math, Guangzhou 510275, Guangdong, Peoples R China

[2] Guangdong Univ Educ, Dept Math, Guangzhou 510303, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2018年 / 465卷 / 02期

关键词：

Completeness; Weighted Stepanov-like pseudo almost automorphic (periodic) functions; rho-Ergodic zero set; ABSTRACT DIFFERENTIAL-EQUATIONS; EVOLUTION-EQUATIONS; BANACH-SPACES;

D O I：

10.1016/j.jmaa.2018.05.057

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the completeness of the space of weighted Stepanov-like pseudo almost automorphic (periodic) functions under weak conditions. That is, for every rho is an element of U-infinity, the space of weighted Stepanov-like pseudo almost automorphic (periodic) functions is complete under the norm parallel to.parallel to(Sp). The main method used is to skillfully construct the decomposition of a function, then a norm inequality is established and to get the related convergent subsequences of Cauchy sequences in the space. (C) 2018 Elsevier Inc. All rights reserved.

引用

页码：1176 / 1185

页数：10

共 26 条

[1] Stepanov-like weighted pseudo almost automorphic solutions to fractional order abstract integro-differential equations [J].

Abbas, Syed ;

Kavitha, V. ;

Murugesu, R. .

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2015, 125 (03) :323-351

[2]

Andres J., 2006, Rend. Mat. Appl., V26, P121

[3] Weighted pseudo almost automorphic functions and applications to abstract differential equations [J].

Blot, J. ;

Mophou, G. M. ;

N'Guerekata, G. M. ;

Pennequin, D. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (3-4) :903-909

[4] NEW APPROACH TO ALMOST PERIODICITY [J].

BOCHNER, S .

PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1962, 48 (12) :2039-&

[5] Stepanov-Like Weighted Pseudo Almost Automorphic Functions Via Measure Theory [J].

Chang, Yong-Kui ;

N'Guerekata, G. M. ;

Zhang, Rui .

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 2016, 39 (03) :1005-1041

[6] Weighted pseudo almost automorphic solutions to a semilinear fractional differential equation with Stepanov-like weighted pseudo almost automorphic nonlinear term [J].

Chang, Yong-Kui ;

Zhang, Mei-Juan ;

Ponce, Rodrigo .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 257 :158-168

[7] Weighted pseudo almost periodic functions and applications [J].

Diagana, Toka .

COMPTES RENDUS MATHEMATIQUE, 2006, 343 (10) :643-646

[8] Existence of weighted pseudo-almost periodic solutions to some classes of differential equations with Sp-weighted pseudo-almost periodic coefficients [J].

Diagana, Toka ;

Mophou, Gisele M. ;

N'Guerekata, Gaston M. .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (01) :430-438

[9] Existence of pseudo-almost automorphic solutions to some abstract differential equations with Sp-pseudo-almost automorphic coefficients [J].

Diagana, Toka .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (11) :3781-3790

[10] Stepanov-like pseudo-almost periodicity and its applications to some nonautonomous differential equations [J].

Diagana, Toka .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (12) :4277-4285

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