INEQUALITIES OF THE 3/8-SIMPSON TYPE FOR DIFFERENTIABLE FUNCTIONS VIA GENERALIZED FRACTIONAL OPERATORS

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Bayraktar B., G.omez L., N.apoles J.

Problemy Analiza, vol.14(32), no.2, pp.25-52, 2025 (ESCI, Scopus)

  • Publication Type: Article / Article
  • Volume: 14(32) Issue: 2
  • Publication Date: 2025
  • Doi Number: 10.15393/j3.art.2025.17330
  • Journal Name: Problemy Analiza
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.25-52
  • Keywords: (h,)–convex function, convex function, H.older inequality, Lipschitz function, Power mean inequality, Simpsontype inequality, weighted integral operator, Young inequality
  • Open Archive Collection: AVESIS Open Access Collection
  • Bursa Uludag University Affiliated: Yes

Abstract

Simpson-type inequalities are an important tool in mathematical analysis, particularly in the study of integrals. In this paper, we present new generalized 3/8-Simpson-type inequalities for functions whose first derivative modulus is (h, m)-convex and satisfies the Lipschitz condition via weight integral operators. To obtain these results, we use a new integral identity established in our study. This research generalizes, extends, and complements the existing results in the literature.