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<p>The notion of integral means of set-valued maps with values in a Banach space is introduced and investigated. A set-valued counterpart of the classical mean value theorem for integrals is presented. It is also proved that if a set-valued map is convex on an interval <i>I</i> then its integral mean is Schur-convex on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(I^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>I</mi> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>.</p>

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Integral means of set-valued maps

  • 期刊论文

  • 发表日期：

    2025年9月19日

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  • Kazimierz Nikodem

摘要

The notion of integral means of set-valued maps with values in a Banach space is introduced and investigated. A set-valued counterpart of the classical mean value theorem for integrals is presented. It is also proved that if a set-valued map is convex on an interval I then its integral mean is Schur-convex on \(I^2\) I 2 .