Several integral inequalities for (<i>α</i>, <i>s</i>,<i>m</i>)-convex functions
M. Emіn Özdemіr, Saad Ihsan Butt, Bahtiyar Bayraktar, Jamshed Nasir
Abstract
In this paper, we establish several new integral inequalities for (<i>α</i>, <i>s</i>, <i>m</i>)-convex functions. We recapture the Hermite-Hadamard inequality as a particular case. In order to obtain our results, we use classical inequalities such as Hölder inequality, Hölder-Işcan inequality and Power mean inequality. We formulate several bounds involving special functions like classical Euler-Gamma, Beta and PsiGamma functions. We also give some applications.
Topics & Concepts
MathematicsConvex functionInequalityJensen's inequalityRegular polygonYoung's inequalityEuler's formulaHölder's inequalityKantorovich inequalityOrder (exchange)Inequality of arithmetic and geometric meansPure mathematicsMathematical analysisConvex optimizationLinear inequalityConvex analysisGeometryEconomicsFinanceMathematical Inequalities and ApplicationsFunctional Equations Stability Results