scholarly journals Convolutions in (µ, ν)-pseudo-almost periodic and (µ, ν)-pseudo-almost automorphic function spaces and applications to solve integral equations

Cubo (Temuco) ◽  
2021 ◽  
Vol 23 (1) ◽  
pp. 63-85
Author(s):  
David Békollè ◽  
Khalil Ezzinbi ◽  
Samir Fatajou ◽  
Duplex Elvis Houpa Danga ◽  
Fritz Mbounja Béssémè
Keyword(s):  
Integral Equations ◽  
Function Spaces ◽  
Automorphic Function ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic

scholarly journals Convolutions in µ-pseudo almost periodic and µ-pseudo almost automorphic function spaces and applications to solve Integral equations

2020 ◽  
Vol 7 (1) ◽  
pp. 32-52
Author(s):  
Fritz Mbounja Béssémè ◽  
David Békollè ◽  
Khalil Ezzinbi ◽  
Samir Fatajou ◽  
Duplex Elvis Houpa Danga
Keyword(s):  
Integral Equations ◽  
Evolution Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Convolution Product ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic

AbstractThe aim of this work is to give sufficient conditions ensuring that the space PAP(𝕉, X, µ) of µ-pseudo almost periodic functions and the space PAA(𝕉, X, µ) of µ-pseudo almost automorphic functions are invariant by the convolution product f = k * f, k ∈ L1(𝕉). These results establish sufficient assumptions on k and the measure µ. As a consequence, we investigate the existence and uniqueness of µ-pseudo almost periodic solutions and µ-pseudo almost automorphic solutions for some abstract integral equations, evolution equations and partial functional differential equations.

scholarly journals Discrete Weighted Pseudo Almost Automorphic Solutions of Nonautonomous Difference Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-8
Author(s):  
Xiaoqing Wen ◽  
Hongwei Yin
Keyword(s):  
Difference Equations ◽  
Automorphic Function ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Pseudo Almost Automorphic

We introduce the concept of a discrete weighted pseudo almost automorphic function and prove some basic results. Further, we investigate the nonautonomous linear and semilinear difference equations and obtain the weighted pseudo almost automorphic solutions of both these kinds of difference equations, respectively. Our results generalize the ones by Lizama and Mesquita (2013).

scholarly journals Pseudo almost periodic and automorphic mild solutions to nonautonomous neutral partial evolution equations

2015 ◽  
Vol 2 (1) ◽  
Author(s):  
Abdelkarim-Nidal Akdad ◽  
Khalil Ezzinbi ◽  
Lotti Souden
Keyword(s):  
Existence Result ◽  
Evolution Equations ◽  
Mild Solutions ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic ◽  
Automorphic Functions

AbstractIn this work, we present a new concept of Stepanov weighted pseudo almost periodic and automorphic functions which is more generale than the classical one, and we obtain a new existence result of μ-pseudo almost periodic and μ-pseudo almost automorphic mild solutions for some nonautonomous evolution equations with Stepanov μ-pseudo almost periodic terms. An example is shown to illustrate our results.

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