Noor-ul-AinCIIT/SP24-RMT-015/LHRDr. SAAD IHSAN BUTTLHR TP 100762026-05-142025https://repository.cuilahore.edu.pk/123456789/3909In this work, we consider the concept of strongly multiplicatively harmonic convex function (SMHCf ). We establish integral inequalities of Hermite-Hadamard (HH) type inequalities for the product and quotient results, in the frame of multiplicative calculus. We discuss the characteristics of SMHCf function. Further, we derive inequalities of trapezoid and mid- point type. In addition, we also verify the validity of our results by graphical descriptions. Also, we enhance our research by offering various applications to specialfunctions.enDepartment of MathematiccsSP24MathematiccsHarmonic multiplicative fractional integralFractional calculusIntegral inequalitiesDr. SAAD IHSAN BUTTThesis