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In this chapter, we prove some new inequalities of Hermite-Hadamard-type for r-convex functions on an arbitrary time scale using the diamond- \(\alpha \) dynamic integrals, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend and improve some known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogs.

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Dynamic Hermite-Hadamard Inequality for r-Convex Symmetric Functions on Time Scales and Their Applications

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  • 发表日期：

    2025年

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  • Ahmed A. El-Deeb,
  • Sandra Pinelas

摘要

In this chapter, we prove some new inequalities of Hermite-Hadamard-type for r-convex functions on an arbitrary time scale using the diamond- \(\alpha \) dynamic integrals, which is defined as a linear combination of the delta and nabla integrals. These inequalities extend and improve some known dynamic inequalities on time scales and unify and extend some continuous inequalities and their corresponding discrete analogs.