Search

In this paper, we proved two new Riemann–Liouville fractional Hermite–Hadamard type inequalities for harmonically convex functions using the left and right fractional integrals independently. Also, we have two new Riemann–Liouville fractional trapezoidal type identities for differentiable functions. Using these identities, we obtained some new trapezoidal type inequalities for harmonically convex functions. Our results generalize the results given by İşcan (Hacet J Math Stat 46(6):935–942, 2014). [ABSTRACT FROM AUTHOR]

The authors discover a new identity concerning differentiable mappings defined on m -invex set via general fractional integrals. Using the obtained identity as an auxiliary result, some fractional integral inequalities for generalized- m - ((h 1 p , h 2 q) ; (η 1 , η 2)) -convex mappings by involving an extended generalized Mittag–Leffler function are presented. It is pointed out that some new special cases can be deduced from main results. Also these inequalities have some connections with known integral inequalities. At the end, some applications to special means for different positive real numbers are provided as well. [ABSTRACT FROM AUTHOR]

Using an extension of Montgomery's identity and the Green's function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum ∑ i = 1 m ρ i h (λ i) and the integral ∫ a b ρ (λ) h (γ (λ)) d λ where h is an n-convex function. [ABSTRACT FROM AUTHOR]