IMPROVEMENT OF FRACTIONAL HERMITE- HADAMARD TYPE INEQUALITY FOR CONVEX FUNCTIONS

KUNT M., İŞCAN İ., TURHAN S., KARAPINAR D.

MISKOLC MATHEMATICAL NOTES, cilt.19, sa.2, ss.1007-1017, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 19 Sayı: 2
  • Basım Tarihi: 2018
  • Doi Numarası: 10.18514/mmn.2018.2441
  • Dergi Adı: MISKOLC MATHEMATICAL NOTES
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1007-1017
  • Anahtar Kelimeler: convex functions, Hermite-Hadamard inequalities, Riemann-Liouville fractional integrals, midpoint type inequalities
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this paper, it is proved that fractional Hermite-Hadamard inequality and fractional Hermite-Hadamard-Fejer inequality are just results of Hermite-Hadamard-Fejer inequality. After this, a new fractional Hermite-Hadamard inequality which is not a result of Hermite-Hadamard-Fejer inequality and better than given in [9] by Sarikaya et al. is obtained. Also, a new equality is proved and some new fractional midpoint type inequalities are given. Our results generalizes the results given in [5] by Kirmaci.