Some inequalities using generalized convex functions in quantum analysis

Abstract:

In the present work, the Hermite-Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in (0, 1] and two arbitrary real functions defined on [0, 1]. From the proven results, various inequalities of the same type are deduced for other types of generalized convex functions and the methodology used reveals, in a sense, a symmetric mathematical phenomenon. In addition, the definition of dominated convex functions with respect to the generalized class of convex functions aforementioned is introduced, and some integral inequalities are established.

Año de publicación:

2019

Keywords:

• Integral inequalities
• (m, h , h )-convex functions 1 2
• Quantum calculus
• Dominated convexity

Fuente:

google

scopus