Hermite–Hadamard Type Inequalities via Generalized Harmonic Exponential Convexity and Applications
Saad Ihsan Butt, Muhammad Tariq, Adnan Aslam, Hijaz Ahmad, Taher A. Nofal
Abstract
In this work, we introduce the idea and concept of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" id="M1"> <a:mi>m</a:mi> </a:math> –polynomial <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" id="M2"> <c:mi>p</c:mi> </c:math> –harmonic exponential type convex functions. In addition, we elaborate the newly introduced idea by examples and some interesting algebraic properties. As a result, several new integral inequalities are established. Finally, we investigate some applications for means. The amazing techniques and wonderful ideas of this work may excite and motivate for further activities and research in the different areas of science.
Topics & Concepts
Hermite polynomialsConvexityHadamard transformMathematicsExponential functionType (biology)Exponential typeHarmonicInequalityPure mathematicsApplied mathematicsMathematical analysisPhysicsGeologyEconomicsPaleontologyQuantum mechanicsFinancial economicsMathematical Inequalities and ApplicationsMathematical functions and polynomialsFunctional Equations Stability Results