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, cilt.37, ss.461-474, 2019 (ESCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 37 Konu: 2
  • Basım Tarihi: 2019
  • Dergi Adı: SIGMA JOURNAL OF ENGINEERING AND NATURAL SCIENCES-SIGMA MUHENDISLIK VE FEN BILIMLERI DERGISI
  • Sayfa Sayıları: ss.461-474

Özet

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.