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<p>In the present paper we introduce a notion of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-convexity which is a common generalization of the notion of convexity, Wright-convexity, strong convexity and many others. We introduce a notion of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-derivative which is connected to <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-convex functions and we examine its properties. In the last section of the paper we give conditions which assure the continuity of an arbitrary <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-convex function.</p>

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On some generalization of Wright-convex functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月31日

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  • Andrzej Olbryś

摘要

In the present paper we introduce a notion of \(\gamma \) γ -convexity which is a common generalization of the notion of convexity, Wright-convexity, strong convexity and many others. We introduce a notion of \(\gamma \) γ -derivative which is connected to \(\gamma \) γ -convex functions and we examine its properties. In the last section of the paper we give conditions which assure the continuity of an arbitrary \(\gamma \) γ -convex function.