GENERALIZED PETROVIČ INEQUALITY AND ITS RELATED ESTIMATIONS IN SUPERQUADRATICITY ON THE FRACTAL SPACE WITH APPLICATIONS

Saad Ihsan Butt (), Dawood Khan (), Sanja Tipuriä†-Spuå½eviä† () and Youngsoo Seol
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Saad Ihsan Butt: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Dawood Khan: Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Pakistan
Sanja Tipuriä†-Spuå½eviä†: Faculty of Chemistry and Technology, University of Split, Rudera BoÅ¡kovića 35, Split 21000, Croatia
Youngsoo Seol: Department of Mathematics, Dong-A University, Busan 49315, Korea

FRACTALS (fractals), 2025, vol. 33, issue 09, 1-24

Abstract: This study considers the concept of generalized superquadratic functions within fractal spaces. The inequalities derived from these functions demonstrate greater precision compared to those obtained from convex functions. The work begins with the presentation of the generalized PetroviÄ inequality in fractal spaces. Two identities for differentiable generalized superquadratic functions are then established. Using these identities and the generalized PetroviÄ inequality, fractal versions of midpoint and trapezoid-type inequalities are derived for differentiable generalized superquadratic functions. The findings are supported by reduced cases and graphical representations based on select examples. Additionally, the research is enriched by incorporating special means and functions within fractal spaces. These results contribute significantly to the existing literature, providing enhanced insights and extending the understanding of inequalities in fractal contexts.

Keywords: Fractal Set; Generalized Superquadratic Function; Generalized PetroviÄ Inequality; Generalized Midpoint-type Inequality; Generalized Trapezoid-type Inequality; Mittag-Leffler Function (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0218348X25500860

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