IMPROVED HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS VIA KATUGAMPOLA FRACTIONAL INTEGRALS


Sanli Z., KUNT M., KÖROĞLU T.

SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI, vol.37, no.2, pp.461-474, 2019 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2019
  • Journal Name: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Academic Search Premier, Directory of Open Access Journals
  • Page Numbers: pp.461-474
  • Keywords: Hermite-Hadamard inequalities, Katugampola fractional integrals, convex functions, DIFFERENTIABLE MAPPINGS
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, we gave adjustments for some results in the paper [1], and proved three new Katugampola fractional Hermite-Hadamard type inequalities for convex functions by using the left and the right fractional integrals independently. One of our Katugampola fractional Hermite-Hadamard type inequalities is better than given by Chen and Katugampola. Also, we gave two new Katugampola fractional identities for differentiable functions. By using these identities, we obtained some new trapezoidal type inequalities for convex functions. Our results generalize earlier results.