Novel fractional integral inequalities for GA-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.svg" display="inline" id="d1e222"><mml:mrow><mml:mi>C</mml:mi><mml:mi>r</mml:mi></mml:mrow></mml:math>-convex functions and connections with information systems

Fahad, Asfand; Ali, Zammad; Furuichi, Shigeru; Wang, Yuanheng

doi:10.1016/j.aej.2024.11.034

Alexandria Engineering Journal

2025

DOI: 10.1016/j.aej.2024.11.034

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Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems

Asfand Fahad,

Zammad Ali,

Shigeru Furuichi

et al.

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New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities

Fahad,

Ali,

Furuichi

et al. 2024

Fractal Fract

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We prove the inequalities of the weighted Hermite–Hadamard type the and Hermite–Hadamard–Mercer type for an extremely rich class of geometrically arithmetically-h-convex functions (GA-h-CFs) via generalized Hadamard–Fractional integral operators (HFIOs). The two generalized fractional integral operators (FIOs) are Hadamard proportional fractional integral operators (HPFIOs) and Hadamard k-fractional integral operators (HKFIOs). Moreover, we also present the results for subclasses of GA-h-CFs and show that the inequalities proved in this paper unify the results from the recent related literature. Furthermore, we compare the two generalizations in view of the fractional operator parameters that contribute to the generalizations of the results and assess the better approximation via graphical tools. Finally, we present applications of the new inequalities via HPFIOs and HKFIOs by establishing interpolation relations between arithmetic mean and geometric mean and by proving the new upper bounds for the Tsallis relative operator entropy.

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New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities

Fahad,

Ali,

Furuichi

et al. 2024

Fractal Fract

View full text Add to dashboard Cite

show abstract

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Novel fractional integral inequalities for GA-Cr-convex functions and connections with information systems

Cited by 1 publication

References 31 publications

New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities

New Inequalities for GA–h Convex Functions via Generalized Fractional Integral Operators with Applications to Entropy and Mean Inequalities

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