Doss ρ-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula>n

In this paper, we investigate various classes of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type...

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Autores principales:	Marko Kostić, Wei-Shih Du, Vladimir E. Fedorov
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Doss <i>ρ</i>-almost periodic type functions in ℝ<sup><i>n</i></sup> Lebesgue spaces with variable exponents abstract Volterra integro-differential equations Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/1cfb2a52efde411cadce97ce5aca5998
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spelling	oai:doaj.org-article:1cfb2a52efde411cadce97ce5aca59982021-11-11T18:21:10ZDoss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>10.3390/math92128252227-7390https://doaj.org/article/1cfb2a52efde411cadce97ce5aca59982021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2825https://doaj.org/toc/2227-7390In this paper, we investigate various classes of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>:</mo><mi mathvariant="sans-serif">Λ</mi><mo>×</mo><mi>X</mi><mo>→</mo><mi>Y</mi><mo>,</mo></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∅</mo><mo>≠</mo><mi mathvariant="sans-serif">Λ</mi><mo>⊆</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>n</mi></msup><mo>,</mo></mrow></semantics></math></inline-formula><i> X</i> and <i>Y</i> are complex Banach spaces, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> is a binary relation on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mo>.</mo></mrow></semantics></math></inline-formula> We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>c</mi><mo>)</mo></mrow></semantics></math></inline-formula>-periodic functions and Weyl-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given.Marko KostićWei-Shih DuVladimir E. FedorovMDPI AGarticleDoss <i>ρ</i>-almost periodic type functions in ℝ<sup><i>n</i></sup>Lebesgue spaces with variable exponentsabstract Volterra integro-differential equationsMathematicsQA1-939ENMathematics, Vol 9, Iss 2825, p 2825 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Doss <i>ρ</i>-almost periodic type functions in ℝ<sup><i>n</i></sup> Lebesgue spaces with variable exponents abstract Volterra integro-differential equations Mathematics QA1-939
spellingShingle	Doss <i>ρ</i>-almost periodic type functions in ℝ<sup><i>n</i></sup> Lebesgue spaces with variable exponents abstract Volterra integro-differential equations Mathematics QA1-939 Marko Kostić Wei-Shih Du Vladimir E. Fedorov Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
description	In this paper, we investigate various classes of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions of the form <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>F</mi><mo>:</mo><mi mathvariant="sans-serif">Λ</mi><mo>×</mo><mi>X</mi><mo>→</mo><mi>Y</mi><mo>,</mo></mrow></semantics></math></inline-formula> where <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>∈</mo><mi mathvariant="double-struck">N</mi><mo>,</mo></mrow></semantics></math></inline-formula><inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>∅</mo><mo>≠</mo><mi mathvariant="sans-serif">Λ</mi><mo>⊆</mo><msup><mrow><mi mathvariant="double-struck">R</mi></mrow><mi>n</mi></msup><mo>,</mo></mrow></semantics></math></inline-formula><i> X</i> and <i>Y</i> are complex Banach spaces, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula> is a binary relation on <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>Y</mi><mo>.</mo></mrow></semantics></math></inline-formula> We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions, like the translation invariance, the convolution invariance and the invariance under the actions of convolution products, are clarified. We examine connections of Doss <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>ω</mi><mo>,</mo><mi>c</mi><mo>)</mo></mrow></semantics></math></inline-formula>-periodic functions and Weyl-<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>ρ</mi></semantics></math></inline-formula>-almost periodic type functions in the multi-dimensional setting. Certain applications of our results to the abstract Volterra integro-differential equations and the partial differential equations are given.
format	article
author	Marko Kostić Wei-Shih Du Vladimir E. Fedorov
author_facet	Marko Kostić Wei-Shih Du Vladimir E. Fedorov
author_sort	Marko Kostić
title	Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
title_short	Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
title_full	Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
title_fullStr	Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
title_full_unstemmed	Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
title_sort	doss <i>ρ</i>-almost periodic type functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">r</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/1cfb2a52efde411cadce97ce5aca5998
work_keys_str_mv	AT markokostic dossirialmostperiodictypefunctionsininlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasupinisup AT weishihdu dossirialmostperiodictypefunctionsininlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasupinisup AT vladimirefedorov dossirialmostperiodictypefunctionsininlineformulamathdisplayinlinesemanticsmrowmimathvariantdoublestruckrmimrowsemanticsmathinlineformulasupinisup
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Doss <i>ρ</i>-Almost Periodic Type Functions in <inline-formula><math display="inline"><semantics><mrow><mi mathvariant="double-struck">R</mi></mrow></semantics></math></inline-formula><sup><i>n</i></sup>

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