Title of article :
Positivity of Integrals for Higher Order ∇-Convex and Completely Monotonic Functions
Author/Authors :
Mehmood ، Faraz Department of Mathematics - Dawood University of Engineering and Technology , Khan ، Asif reza Department of Mathematics - University of Karachi , Adnan ، Muhammad Department of Mathematics - University of Karachi
Abstract :
We extend the definitions of ∇−convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals ∫ P(y)f(y)dy and ∫ ∫ P(y, z)f(y, z)dydz are deduced. Using obtained identities, positivity of these expressions are characterized for higher order ∇−convex and completely monotonic functions. Some applications in terms of generalized Cauchy means and exponential convexity are given.
Keywords :
Convex functions , ∇−convex functions , Completely monotonic functions
Journal title :
Sahand Communications in Mathematical Analysis
Journal title :
Sahand Communications in Mathematical Analysis
