New Quantum Hermite-Hadamard Inequalities Utilizing Harmonic Convexity of the Functions

Abstract

The aim of this paper is to obtain some new Hermite-Hadamard type of inequalities via harmonic convex, strongly harmonic convex, strongly harmonic log-convex functions, and AH-convex in connection with quantum calculus. All the results reduce to ordinary calculus case when q → 1 − .

New quantum boundaries for quantum Simpson’s and quantum Newton’s type inequalities for preinvex functions

“…In 2013, Tariboon introduced using classical convexity. Many mathematicians have done studies in q-calculus analysis; the interested reader can check [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Post-quantum Hermite–Hadamard type inequalities for interval-valued convex functions

“…In 2004, Rajkovic gave a definition of the Riemann-type q-integral which was a generalization of Jackson q-integral. In 2013, Tariboon introduced mathematicians have done studies in q-calculus analysis, the interested reader can check [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

On Hermite–Hadamard-Type Inequalities for Coordinated h-Convex Interval-Valued Functions

“…Due to its key role in convex analysis, the H-H inequality has been used as a powerful tool to acquire a large number of nice results in integral inequalities and optimization theory. Recently, it has been generalized by means of different types of convexity, such as s-convex functions [1][2][3][4], log-convex [5][6][7], harmonic convexity [8], and especially for h-convex functions [9]. Since 2007, various extensions and generalizations of H-H inequalities for h-convex functions have been established in [10][11][12][13][14][15][16].…”