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>
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...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
MDPI AG
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/1cfb2a52efde411cadce97ce5aca5998 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | 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. |
|---|