New inequalities for co-ordinated convex functions via Riemann-Liouville fractional calculus

Abstract

We provide some new Hermite-Hadamard type inequalities for co-ordinated convex functions, via Riemann-Liouville fractional integration.

On new generalized inequalities with some parameters for coordinated convex functions via generalized fractional integrals

“…where Θ(𝜅 1 , 𝜅 2 ; 𝜅 3 , 𝜅 4 ) is defined as in Lemma 1 and Π 𝜑 1 , ∇ 𝜓 i , i = 1, 2, are defined as in (14).…”

“…11 For the other similar inequalities, please refer to previous works. [12][13][14][15][16][17][18][19][20][21] On the other hand, the following inequality is well-known in the literature as Simpson's inequality.…”

“…What's more, Turkay et al defined the generalized fractional integrals for functions with two variables, and they presented Hermite–Hadamard and trapezoid type inequalities for this kind of fractional integrals 11 . For the other similar inequalities, please refer to previous works 12–21 …”

On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals

“…These authors presented Hermite-Hadamard and trapezoidal type inequalities for this kind of fractional integrals in [47]. For the other similar inequalities, we refer to [14,15,25,30,33,45].…”

Some generalized fractional trapezoid and Ostrowski type inequalities for functions with bounded partial derivatives

“…Tunç et al 40 presented some fractional midpoint type inequalities for coordinated convex functions For the other similar inequalities, please refer to previous studies. [41][42][43][44][45][46][47][48][49] The aim of this paper is to establish some trapezoid and Ostrowski type inequalities for generalized fractional integrals. The general structure of the paper consists of six chapters including an introduction.…”