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 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 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.

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.

V.—Les transformations asymptotiquement presque périodiques discontinues et le lemme ergodique. (Première Note.)

1950 ◽  
Vol 63 (1) ◽  
pp. 61-68
Author(s):  
Maurice Fréchet
Keyword(s):  
Ergodic Theorem ◽  
Continuous Functions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Discontinuous Functions ◽  
Extended Class ◽  
Class Of Functions ◽  
Asymptotically Almost Periodic

SynopsisWith the aim of establishing, under wide conditions, the ergodic theorem of G. D. Birkhoff, the author extends the class of asymptotically almost-periodic functions, considering now not only continuous functions, as he had already done in 1943, but discontinuous functions. Definitions and properties of the extended class of functions are set out, some comparisons being made with almost-periodic functions in the sense of Bohr, Stepanoff, Weyl and Besicovitch. Applications to the ergodic theorem are adumbrated.

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.

Sign in / Sign up

Export Citation Format

Share Document