Integral inequalities for two-dimensional pq-convex functions

Abstract

In this paper, we introduce the concept of two dimensional pq-convex functions. We establish several new Hermite-Hadamard inequalities for two dimensional pq-convex functions. Some special cases are also discussed. Results obtained in this paper can be viewed as significant extensions of the previously known results.

On Hermite-Hadamard type inequalities of coordinated (p1,h1)-(p2,h2)-convex functions via Katugampola fractional integrals

“…Multiplying (13) by Remark 3.3. If h 1 (t) = t = h 2 (t) and α = β = 1, then above result coincide to Theorem 2.8 which was proved in [21]. Remark 3.4.…”

“…al. [21] introduced the notion of coordinated pq-convex functions to generalize the p-convex functions as follows:…”

“…Noor et al [21] defined a new class of functions named as two dimensional(coordinated) pq-convex functions. They generalize some inequalities for this class of functions.…”

Some integral inequalities for p-convex functions

“…The classical concept of convex sets and convex functions has been extended in different directions using various novel approaches, see [3,4,[7][8][9][10][11][12][13][14][15][16][17][18]25]. Motivated by this Zhang et al [25] introduced an interesting class of convex functions which is called p-convex functions.…”

“…Motivated by this Zhang et al [25] introduced an interesting class of convex functions which is called p-convex functions. For some recent investigations and extensions of p-convex functions, see [8,15,25]. Theory of convex functions and theory of inequalities are very closely related to each other.…”