This paper proves a new q-Hermite-Hadamard inequality for convex functions using quantum integrals. We also prove some new midpoint-type inequalities for q-differentiable convex functions. Moreover, we present some examples to illustrate our established results, supplemented with graphs. [ABSTRACT FROM AUTHOR]
In this paper, we introduce the notion of (p,ϕh)-convex functions and present some properties and representation of such functions. Finally, a version of Hermite Hadamard-type inequalities for (p,ϕh)-convex functions are established. [ABSTRACT FROM AUTHOR]
NOOR, MUHAMMAD ASLAM, NOOR, KHALIDA INAYAT, and AWAN, MUHAMMAD UZAIR
Subjects
*GENERALIZATION, *MATHEMATICAL inequalities, *CONVEX functions, *FRACTIONAL integrals, *RIEMANN integral
Abstract
In this paper, we derive some Hermite-Hadamard type inequalities via s-convex functions of first and second sense respectively. These inequalities involve k-Riemann-Liouville fractional integrals. We also discuss some special cases. [ABSTRACT FROM AUTHOR]
In this paper, we prove Hermite-Hadamard inequality for uniformly convex, uniformly s-convex functions. Also, we obtain Hermite Hadamard inequality for fractional integral by using these functions. Finally, some applications of these inequalities are given. [ABSTRACT FROM AUTHOR]