FRACTAL-FRACTIONAL MILNE-TYPE INEQUALITIES VIA GENERALIZED HARMONIC CONVEXITY
Fractals, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1142/s0218348x2650115x
- Dergi Adı: Fractals
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, Compendex, INSPEC, zbMATH, Academic Search Ultimate (EBSCO), Engineering Source (EBSCO), Technology Collection (ProQuest)
- Anahtar Kelimeler: Fractal-Fractional Calculus, Generalized Harmonic Convexity, Generalized Hölder’s Inequality, Generalized Power Mean Inequality, Milne’s Inequalities
- Kocaeli Üniversitesi Adresli: Evet
Özet
This paper explores the development of fresh mathematical inequalities operating under the umbrella of local fractional calculus. A central breakthrough of our research is the formulation of an innovative auxiliary fractal-fractional identity. Building upon this foundational equation, we deduce a series of new Milne-type bounds, tailored for mappings that possess generalized harmonically convex first-order local fractional derivatives. To expand the analytical reach of our study, we extract supplementary bounding constraints by deploying the generalized power mean and Hölder inequalities. Moreover, the theoretical propositions are strictly substantiated using a comprehensive numerical example; accompanying visual plots are supplied to verify the accuracy and reliability of the generated boundaries. Concluding the study, the tangible applicability of our newly constructed estimations is showcased through a specific implementation concerning distinct fractal averages.