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


Sanli Z. , KÖROĞLU T. , KUNT M.

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS, cilt.68, sa.2, ss.1556-1575, 2019 (ESCI İndekslerine Giren Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 68 Konu: 2
  • Basım Tarihi: 2019
  • Doi Numarası: 10.31801/cfsuasmas.413019
  • Dergi Adı: COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS
  • Sayfa Sayıları: ss.1556-1575

Özet

In this paper, we prove three new Katugampola fractional Hermite-Hadamard type inequalities for harmonically 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 in [17]. Also, we give two new Katugampola fractional identities for differentiable functions. By using these identities, we obtain some new trapezoidal type inequalities for harmonically convex functions. Our results generalize many results from earlier papers.