THE RIGHT RIEAMAN-LIOUVILLE FRACTIONAL HERMITE-HADAMARD TYPE INEQUALITIES FOR CONVEX FUNCTIONS

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

JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS, vol.9, no.1, pp.45-57, 2018 (ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 1
  • Publication Date: 2018
  • Journal Name: JOURNAL OF INEQUALITIES AND SPECIAL FUNCTIONS
  • Journal Indexes: Emerging Sources Citation Index (ESCI)
  • Page Numbers: pp.45-57
  • Keywords: Convex functions, Hermite-Hadamard inequality, Right Rieaman-Liouville fractional integral, Trapezoid type inequalities, Midpoint type inequalities, DIFFERENTIABLE MAPPINGS, REAL NUMBERS, FORMULA
  • Karadeniz Technical University Affiliated: Yes

Abstract

In this paper, with a new approach, a new fractional Hermite-Hadamard type inequality for convex functions is obtained by using only the right 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 the studies [1, 4, 6]. We expect that this study will be lead to the new fractional integration studies for Hermite-Hadamard type inequalities.