On Fractional Milne-Mercer Bounds for s-Convex Functions with Applications

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Munir A., BUDAK H., Kashuri A., Butt S. I.

Universal Journal of Mathematics and Applications, cilt.9, sa.3, ss.150-166, 2026 (Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 9 Sayı: 3
  • Basım Tarihi: 2026
  • Doi Numarası: 10.32323/ujma.1918223
  • Dergi Adı: Universal Journal of Mathematics and Applications
  • Derginin Tarandığı İndeksler: Scopus, Applied Science & Technology Source, Central & Eastern European Academic Source (CEEAS), Directory of Open Access Journals
  • Sayfa Sayıları: ss.150-166
  • Anahtar Kelimeler: Bounded function, Hölder’s inequality, Lipschitz function, Milne-Mercer type, Modified Bessel function, Power-mean inequality, q-digamma function, Riemann-Liouville fractional integrals, s-convex function
  • Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
  • Kocaeli Üniversitesi Adresli: Evet

Özet

Fractional integral inequalities play a fundamental role in modern analysis and have significant applications in the qualitative study of fractional differential and integral equations. Motivated by the need for sharper estimates in fractional settings, this paper establishes several new Milne-Mercer type inequalities involving the Riemann-Liouville fractional integral operators. By employing the theory of s-convex functions, we derive a unified framework that extends and generalizes a variety of classical Mercer-type inequalities available in the literature. Furthermore, refined estimates are obtained for bounded functions and functions satisfying Lipschitz-type conditions. The proposed results not only recover numerous known inequalities as particular cases but also provide stronger bounds within the fractional calculus setting. To illustrate the applicability and effectiveness of the theoretical findings, graphical examples are presented. In addition, applications to quadrature formulas, q-digamma functions, and modified Bessel functions are discussed, demonstrating the broad utility of the developed inequalities. The results contribute to the ongoing development of fractional integral inequalities and offer new tools for the analysis of special functions and related problems in applied mathematics.