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\begin{document}

\title{Stepanov pseudo almost periodic functions and applications}



\author[1]{Kamal Khalil}%
\author[2]{Marko Kostic}%
\author[3]{Manuel Pinto}%
\affil[1]{Cadi Ayyad University Faculty of Sciences Semlalia}%
\affil[2]{University of Novi Sad Faculty of Technical Sciences}%
\affil[3]{Universidad de Chile Facultad de Ciencias Fisicas y Matematicas}%


\vspace{-1em}



  
  \date{June 14, 2024}


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\begin{abstract}
In this work, we present basic results and applications of Stepanov
pseudo almost periodic functions with measure. Using only the continuity
assumption, we prove a new composition result of
\$\textbackslash{}mu\$-pseudo almost periodic functions in Stepanov
sense. Moreover, we present different applications to semilinear
differential equations and inclusions in Banach spaces with weak regular
forcing terms. We prove the existence and uniqueness of
\$\textbackslash{}mu\$-pseudo almost periodic solutions (in the strong
sense) to a class of semilinear fractional inclusions and semilinear
evolution equations, respectively, provided that the nonlinear forcing
terms are only Stepanov \$ \textbackslash{}mu \$-pseudo almost periodic
in the first variable and not a uniformly strict contraction with
respect to the second argument. Some examples illustrating our
theoretical results are also presented.%
\end{abstract}%



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\verb`KhKoPi_20.tex`  available at \url{https://authorea.com/users/374521/articles/492058-stepanov-pseudo-almost-periodic-functions-and-applications}

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