HYPERBOLIC TYPE HARMONICALLY CONVEX FUNCTION AND INTEGRAL INEQUALITIES

HYPERBOLIC TYPE HARMONICALLY CONVEX FUNCTION AND INTEGRAL INEQUALITIES

B. Kodamasingh, M. Tariq, S. K. Sahoo, H. Ahmad, J. Nasir

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Abstract

In this paper, we de ne a new class of harmonic convexity i.e. Hyperbolic type harmonic convexity and explore its algebraic properties. Employing this new de nition, 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.

Keywords

Hyperbolic type Convex function,fractional calculus, Holder integral inequality, Hermite-Hadamard inequality.