New extensions of Hermite-Hadamard inequality using k−fractional Caputo derivatives

Nápoles J. E., BAYRAKTAR B.

Advanced Studies: Euro-Tbilisi Mathematical Journal, vol.16, no.2, pp.11-28, 2023 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 16 Issue: 2
  • Publication Date: 2023
  • Doi Number: 10.32513/asetmj/193220082314
  • Journal Name: Advanced Studies: Euro-Tbilisi Mathematical Journal
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.11-28
  • Keywords: Hermite-Hadamard inequality, Caputo fractional derivatives, (h, m)-convex modified functions, MERCER TYPE INEQUALITIES, INTEGRAL-INEQUALITIES, S)-CONVEX, PROOF, (H
  • Bursa Uludag University Affiliated: Yes

Abstract

By means of Caputo k−fractional derivatives, in this work, we obtain new extensions of the Hermite-Hadamard inequality for modified (h, m)− convex functions of the second type. At work, we show that some known results from the literature can be obtained as particular cases of the results presented here.