scholarly journals Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 928 ◽  
Author(s):  
Marko Kostić ◽  
Wei-Shih Du
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces ◽  
Recurrent Functions ◽  
Convolution Products

In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract semilinear integro-differential inclusions in Banach spaces.

scholarly journals Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents, Part II

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1052
Author(s):  
Marko Kostić ◽  
Wei-Shih Du
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Variable Exponent ◽  
Almost Periodicity ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Fractional Differential Inclusions ◽  
Lebesgue Spaces ◽  
Fractional Differential ◽  
Recurrent Type

In this paper, we introduce and analyze several different notions of almost periodic type functions and uniformly recurrent type functions in Lebesgue spaces with variable exponent L p ( x ) . We primarily consider the Stepanov and Weyl classes of generalized almost periodic type functions and generalized uniformly recurrent type functions. We also investigate the invariance of generalized almost periodicity and generalized uniform recurrence with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract fractional differential inclusions in Banach spaces.

scholarly journals Almost periodic and asymptotically almost periodic type functions in Lebesgue spaces with variable exponents Lp(x)

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1629-1644
Author(s):  
Toka Diagana ◽  
Marko Kostic
Keyword(s):  
Differential Equations ◽  
Banach Spaces ◽  
Almost Periodic Functions ◽  
Important Class ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces ◽  
Asymptotically Almost Periodic

In this paper we introduce and analyze an important class of (asymptotically) Stepanov almost periodic functions in the Lebesgue spaces with variable exponents, which generalizes in a natural fashion all the (asymptotically) almost periodic functions. We then make extensive use of these new functions to study some abstract Volterra integro-differential equations in Banach spaces including multi-valued ones.

scholarly journals Doss ρ-Almost Periodic Type Functions in Rn

Mathematics ◽  
2021 ◽  
Vol 9 (21) ◽  
pp. 2825
Author(s):  
Marko Kostić ◽  
Wei-Shih Du ◽  
Vladimir E. Fedorov
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Banach Spaces ◽  
Binary Relation ◽  
General Setting ◽  
Translation Invariance ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces

In this paper, we investigate various classes of multi-dimensional Doss ρ-almost periodic type functions of the form F:Λ×X→Y, where n∈N, ∅≠Λ⊆Rn,X and Y are complex Banach spaces, and ρ is a binary relation on Y. We work in the general setting of Lebesgue spaces with variable exponents. The main structural properties of multi-dimensional Doss ρ-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 ρ-almost periodic type functions with (ω,c)-periodic functions and Weyl-ρ-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.

Compactness and Almost Periodicity of Multipliers

1983 ◽  
Vol 26 (1) ◽  
pp. 58-62 ◽  
Author(s):  
G. Crombez
Keyword(s):  
Large Class ◽  
Function Spaces ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Weakly Compact ◽  
Banach Function Spaces ◽  
General Method

AbstractThe question as to the existence of nontrivial compact or weakly compact multipliers between spaces of functions on groups has been investigated for several years. Until now, however, no general method which is applicable to a large class of function spaces seems to be knownIn this paper we prove that the existence of nontrivial compact multipliers between Banach function spaces on which a group acts is related to the existence of nonzero almost periodic functions.

scholarly journals Notes on almost-periodicity in topological vector spaces

1986 ◽  
Vol 9 (1) ◽  
pp. 201-204 ◽  
Author(s):  
Gaston Mandata N'guérékata
Keyword(s):  
Differential Equations ◽  
Almost Periodic Functions ◽  
Vector Spaces ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Vector Spaces ◽  
Abstract Differential Equations

A study is made of almost-periodic functions in topological vector spaces with applications to abstract differential equations.

On Bohr almost periodicity

1986 ◽  
Vol 99 (3) ◽  
pp. 489-493 ◽  
Author(s):  
Paul Milnes
Keyword(s):  
Periodic Function ◽  
Present Author ◽  
Almost Periodic Functions ◽  
Unusual Feature ◽  
Almost Periodicity ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Almost Automorphic

AbstractThe first examples of Bohr almost periodic functions that are not almost periodic were given by T. -S. Wu. Later, the present author showed that Bohr almost periodic functions could be distal (and not almost periodic) and even merely minimal. Here it is proved that all Bohr almost periodic functions are minimal. The proof yields an unusual feature about the orbit of a Bohr almost periodic function, one which does not characterize Bohr almost periodic functions, but can be used to show that a Bohr almost periodic function f that is point distal must be distal or, if f is almost automorphic, it must be almost periodic. Some pathologies of Bohr almost periodic functions are discussed.

scholarly journals Denjoy-Bochner almost periodic functions

1984 ◽  
Vol 37 (2) ◽  
pp. 205-222 ◽  
Author(s):  
B. K. Pal ◽  
S. N. Mukhopadhyay
Keyword(s):  
Integrable Function ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Bochner Integral ◽  
Periodic Functions ◽  
Integrable Functions

AbstractThe special Denjoy-Bochner integral (the D*B-integral) which are generalisations of Lebesgue-Bochner integral are discussed in [7, 6, 5]. Just as the concept of numerical almost periodicity was extended by Burkill [3] to numerically valued D*- or D-integrable function, we extend the concept of almost periodicity for Banach valued function to Banach valued D*B-integrable function. For this purpose we introduce as in [3] a distance in the space of all D*B-integrable functions with respect to which the D*B-almost periodicity is defined. It is shown that the D*B-almost periodicity shares many of the known properties of the almost periodic Banach valued function [1, 4].

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