ON GENERALIZATIONS OF INTEGRAL INEQUALITIES


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BAYRAKTAR B., Nápoles J., Rabossi F.

Problemy Analiza, vol.12-29, no.2, pp.3-23, 2022 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 12-29 Issue: 2
  • Publication Date: 2022
  • Doi Number: 10.15393/j3.art.2022.11190
  • Journal Name: Problemy Analiza
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.3-23
  • Keywords: convex function, Hermite-Hadamard inequality, Simp-son-type inequality, Lipschitz conditions, Lagrange theorem, Rie-mann-Liouville fractional integral, HERMITE-HADAMARD TYPE, S-CONVEX, DIFFERENTIABLE MAPPINGS, SIMPSONS TYPE, REAL NUMBERS, DERIVATIVES
  • Bursa Uludag University Affiliated: Yes

Abstract

© Petrozavodsk State University, 2022In the present study, several new generalized integral inequalities of the Hadamard and Simpson-type are obtained. The results were obtained for functions whose first and third derivatives are either convex or satisfy the Lipschitz condition or the conditions of the Lagrange theorem. In a particular case, these results not only confirm but also improve some upper bounds, well known in the literature for the Simpson and Hermite-Hadamard-type inequalities.