ANALYTICAL PROPERTIES ON MULTIPLICATIVELY MψA-p-FUNCTIONS AND RELATED MULTIPLICATIVE ψ-HILFER FRACTIONAL TRAPEZOID-TYPE INEQUALITIES

Zongrui Tan () and Tingsong Du
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Zongrui Tan: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China
Tingsong Du: Three Gorges Mathematical Research Center, China Three Gorges University, Yichang 443002, P. R. China†Department of Mathematics, College of Science, China Three Gorges University, Yichang 443002, P. R. China

FRACTALS (fractals), 2025, vol. 33, issue 07, 1-27

Abstract: The primary objective of this study is to explore the properties and inequalities associated with multiplicatively MψA-p-functions. We commence our investigation by introducing the concept of multiplicatively MψA-p-functions, followed by an analysis of their characteristics. Subsequently, we introduce the multiplicative ψ-Hilfer fractional integrals and formulate an identity involving these operators. Based on this identity, we establish some trapezoid-type inequalities that are applicable to multiplicatively MψA-p-functions. Additionally, we provide several illustrative examples to validate our theoretical findings. Finally, we discuss the applications of the obtained outcomes, linking them to numerical quadrature formulas, and special mean value estimates.

Keywords: Multiplicatively MψA-p-Functions; Multiplicative ψ-Hilfer Fractional Integrals; Trapezoid-Type Inequalities (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500598

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