HERMITE–HADAMARD TYPE INEQUALITIES FOR ℏ-CONVEX FUNCTION VIA FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL

Fractals Pub Date : 2024-03-05 DOI:10.1142/s0218348x24500427

HAIYANG CHENG, DAFANG ZHAO, MEHMET ZEKI SARIKAYA

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Abstract

Fractional $q$ -calculus is considered to be the fractional analogs of $q$ -calculus. In this paper, the fuzzy interval-valued Riemann–Liouville fractional (RLF) $q$ -integral operator is introduced. Also new fuzzy variants of Hermite–Hadamard (HH) type and HH–Fejér inequalities, involving $ℏ$ -convex fuzzy interval-valued functions (FIVFs), are presented by making use of the RLF $q$ -integral. The results not only generalize existing findings in the literature but also lay a solid foundation for research on inequalities concerning FIVFs. Moreover, to verify our theoretical findings, numerical examples and imperative graphical illustrations are provided.

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通过 FUZZY INTERVAL-VALUED FRACTIONAL q-INTEGRAL 测量ℏ-反函数的 HERMITE-HADAMARD 类型不等式

分数 q 微积分被认为是 q 微积分的分数类比。本文引入了模糊区间值黎曼-利乌维尔分数（RLF）q-积分算子。同时，通过利用 RLF q 积分，提出了涉及 ℏ 凸模糊带区间值函数 (FIVF) 的 Hermite-Hadamard (HH) 型和 HH-Fejér 不等式的新模糊变体。这些结果不仅概括了现有文献的结论，而且为有关 FIVF 的不等式研究奠定了坚实的基础。此外，为了验证我们的理论发现，还提供了数值示例和必要的图形说明。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Fractals

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