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<p>In this paper, we introduce a class of convexity known as <InlineEquation ID="IEq2"><EquationSource Format="MATHML"><math><msub><mi mathvariant="script">M</mi><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">Ψ</mi><mo>,</mo><mi>m</mi><mo stretchy="false">)</mo></mrow></msub></math></EquationSource><EquationSource Format="TEX">$\mathcal{M}_{(\Psi ,m)}$</EquationSource></InlineEquation>-convexity. First, we investigate multi-term refinements of the inequality associated with <InlineEquation ID="IEq3"><EquationSource Format="MATHML"><math><msub><mi mathvariant="script">M</mi><mrow><mo stretchy="false">(</mo><mi mathvariant="normal">Ψ</mi><mo>,</mo><mi>m</mi><mo stretchy="false">)</mo></mrow></msub></math></EquationSource><EquationSource Format="TEX">$\mathcal{M}_{(\Psi ,m)}$</EquationSource></InlineEquation>-convexity. Then, our results are further enhanced and generalized through the application of weak sub-majorization theory. As applications, we derive novel refinements of the classical Hermite-Hadamard inequality for these notions. These findings expand upon and generalize recent work in the field, including the studies presented in [2, 19]. Our work contributes to the ongoing development of mathematical inequalities and their various applications.</p>

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Jensen and Jensen-Mercer type inequalities for \(\mathcal{M}_{(\Psi ,m)}\)-convex functions

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月2日

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  • Junmei Zuo,
  • Mohamed Amine Ighachane,
  • Yonghui Ren

摘要

In this paper, we introduce a class of convexity known as M(Ψ,m)$\mathcal{M}_{(\Psi ,m)}$-convexity. First, we investigate multi-term refinements of the inequality associated with M(Ψ,m)$\mathcal{M}_{(\Psi ,m)}$-convexity. Then, our results are further enhanced and generalized through the application of weak sub-majorization theory. As applications, we derive novel refinements of the classical Hermite-Hadamard inequality for these notions. These findings expand upon and generalize recent work in the field, including the studies presented in [2, 19]. Our work contributes to the ongoing development of mathematical inequalities and their various applications.