ON MULTIPLICATIVE (s,P)-CONVEXITY AND RELATED FRACTIONAL INEQUALITIES WITHIN MULTIPLICATIVE CALCULUS

Yu Peng () and Tingsong Du
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Yu Peng: 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), 2024, vol. 32, issue 03, 1-32

Abstract: In this paper, we propose a fresh conception about convexity, known as the multiplicative (s,P)-convexity. Along with this direction, we research the properties of such type of convexity. In the framework of multiplicative fractional Riemann–Liouville integrals and under the ∗differentiable (s,P)-convexity, we investigate the multiplicative fractional inequalities, including the Hermite–Hadamard- and Newton-type inequalities. To further verify the validity of our primary outcomes, we give a few numerical examples. As applications, we proffer a number of inequalities of multiplicative type in special means as well.

Keywords: Fractional Multiplicative Calculus; Hermite–Hadamard’s Inequality; Multiplicatively (s; P)-Convex Functions; Newton-type Inequalities (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1142/S0218348X24500488

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