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<p>In this paper, we introduce and analyze several new classes of Stepanov almost periodic type functions <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(F: \Lambda \times X \rightarrow Y\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>F</mi> <mo>:</mo> <mi mathvariant="normal">Λ</mi> <mo>×</mo> <mi>X</mi> <mo stretchy="false">→</mo> <mi>Y</mi> </mrow> </math></EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\emptyset \ne \Lambda \subseteq \mathbb {R}^{n}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">∅</mi> <mo>≠</mo> <mi mathvariant="normal">Λ</mi> <mo>⊆</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>n</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>, <i>X</i> is an arbitrary non-empty set and <i>Y</i> is a sequentially complete locally convex space. We present various applications of the introduced notion in the analysis of the existence and uniqueness of (Stepanov) almost periodic type solutions to the abstract Volterra integro-differential inclusions in locally convex spaces.</p>

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Stepanov Almost Periodic Functions in Locally Convex Spaces

  • 期刊论文

  • 发表日期：

    2026年4月30日

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  • Marko Kostić

摘要

In this paper, we introduce and analyze several new classes of Stepanov almost periodic type functions \(F: \Lambda \times X \rightarrow Y\) F : Λ × X → Y , where \(\emptyset \ne \Lambda \subseteq \mathbb {R}^{n}\) ∅ ≠ Λ ⊆ R n , X is an arbitrary non-empty set and Y is a sequentially complete locally convex space. We present various applications of the introduced notion in the analysis of the existence and uniqueness of (Stepanov) almost periodic type solutions to the abstract Volterra integro-differential inclusions in locally convex spaces.