ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 9 (2020), no.7, 4797–4805 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.9.7.46 SOME INTEGRAL INEQUALITIES OF HERMITE-HADAMARD TYPE FOR PRODUCT HARMONIC CONVEX FUNCTION SOUBHAGYA KUMAR SAHOO AND BIBHAKAR KODAMASINGH 1 ABSTRACT. The objective of this paper is to establish the integral inequalities of Hermite-Hadamard type for product of harmonic convex function of single vari- able and several variables, product of exponential convex function and product of exponential harmonic function. 1. I NTRODUCTION Convex function and convex set have been studied intensively in mathematical engineering, management science and optimization theory. The classical convexity has been extended and generalized in different direction such as invexity by which the variational inequality problems studied on Banach spaces,Hilbert spaces etc. by B.Kodamasingh et al see [4–6]. Hermite-Hadamard type inequality was studied under the various convex functions. Further, it is extended on harmonic convex function by Imdat Iscan see [1]. Many studies have shown that the theory of harmonic convex function is related with the theory of inequalities.By using the harmonically convex function the bounds of the integral of convex function can be easily obtained. Inequalities play an Important role in many branches of sci- ences. A great number of studies have derived that the concept of Harmonic con- vex function is closely related to the concept of Inequalities. One of the most used inequalities for convex function named Hermite Hadamard integral inequality is 1 corresponding author 2010 Mathematics Subject Classification. 26A51, 26D10, 26D15. Key words and phrases. Harmonic convex set,Harmonic convex function, Hermite-Hadamard’s Inequality, Exponentially Convex Function, Exponentially harmonic Convex Function. 4797