Hyperbolic type harmonically convex function and integral inequalities

In this paper, we define a new class of harmonic convexity i.e. Hyperbolic type harmonic convexity and explore its algebraic properties. Employing this new definition, some integral inequalities of Hermite-Hadamard type are presented. Furthermore, we have presented Hermite-Hadamard inequality involving Riemann Liouville fractional integral operator. We believe the ideas and techniques of this paper may inspire further research in various branches of pure and applied sciences.Publisher's Versio

Ostrowski type inequalities for harmonically s-convex functions

The author introduces the concept of harmonically s-convex functions and establishes some Ostrowski type inequalities and Hermite-Hadamard type inequality of these classes of functions.Comment: 11 page

Ostrowski type inequalities for harmonically s-convex functions via fractional integrals

In this paper, a new identity for fractional integrals is established. Then by making use of the established identity, some new Ostrowski type inequalities for harmonically s-convex functions via Riemann--Liouville fractional integral are established.Comment: 14 page

Hermite-Hadamard and Fejér type inequalities for strongly harmonically convex functions

Introducimos la noción de funciones fuertemente armónicas convexas y presentamos algunso ejemplos y propiedades de ésta clase. También, establecemos algunas desigualdades del tipo  Hermite-Hadamard and y Fejér para la clase introducida.We introduce the notion of strongly harmonically convex function and present some examples and properties of them. We also establish some Hermite-Hadamard and Fej\'er type inequalities for the class of strongly harmonically convex functions which generalizes previous results

Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions

We establish a Fejér type inequality for harmonically convex functions. Our results are the generalizations of some known results. Moreover, some properties of the mappings in connection with Hermite-Hadamard and Fejér type inequalities for harmonically convex functions are also considered

Symmetrized p-convexity and Related Some Integral Inequalities

In this paper, the author introduces the concept of the symmetrized p-convex function, gives Hermite-Hadamard type inequalities for symmetrized p-convex functions.Comment: 13 page