q-微积分中Hermite-Hadamard-Mercer中点和梯形型的一些新不等式

Philosophic research and analysis Pub Date : 2023-06-01 DOI:10.1515/anly-2023-0019

M. Ali, C. Goodrich

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摘要

摘要对于满足Jensen-Mercer不等式(JMI)的函数，我们证明了q- hermite - hadamard - mercer型不等式的一个新变体。此外，我们还利用JMI建立了一些新的可微函数的中点型和梯形型不等式。新发展的不等式也被证明是文献中先前存在的不等式的延伸。

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On some new inequalities of Hermite–Hadamard–Mercer midpoint and trapezoidal type in q-calculus

Abstract In this paper we prove a new variant of q-Hermite–Hadamard–Mercer-type inequality for the functions that satisfy the Jensen–Mercer inequality (JMI). Moreover, we establish some new midpoint- and trapezoidal-type inequalities for differentiable functions using the JMI. The newly developed inequalities are also shown to be extensions of preexisting inequalities in the literature.

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Philosophic research and analysis

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