THE LEFT RIEMANN-LIOUVILLE FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS

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

MATHEMATICA SLOVACA, cilt.69, sa.4, ss.773-784, 2019 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 69 Sayı: 4
  • Basım Tarihi: 2019
  • Doi Numarası: 10.1515/ms-2017-0261
  • Dergi Adı: MATHEMATICA SLOVACA
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.773-784
  • Anahtar Kelimeler: convex functions, Hermite-Hadamard inequalities, left Riemann-Liouville fractional integral, trapezoid type inequalities, midpoint type inequalities, DIFFERENTIABLE MAPPINGS
  • Karadeniz Teknik Üniversitesi Adresli: Evet

Özet

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequalities for convex functions is obtained by using only the left Riemann-Liouville fractional integral. Also, to have new fractional trapezoid and midpoint type inequalities for the differentiable convex functions, two new equalities are proved. Our results generalize earlier studies. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.