TY - JOUR
ID - 249585
TI - Positivity of Integrals for Higher Order $\nabla-$Convex and Completely Monotonic Functions
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Mehmood, Faraz
AU - Khan, Asif Raza
AU - Adnan, Muhammad
AD - Department of Mathematics, Dawood University of Engineering and Technology, New M. A. Jinnah Road, Karachi-74800, Pakistan.
AD - Department of Mathematics, University of Karachi, University Road, Karachi-75270 Pakistan.
Y1 - 2022
PY - 2022
VL - 19
IS - 1
SP - 119
EP - 137
KW - Convex functions
KW - $nabla-$convex functions
KW - completely monotonic functions
DO - 10.22130/scma.2021.527460.926
N2 - We extend the definitions of $\nabla-$convex and completely monotonic functions for two variables. Some general identities of Popoviciu type integrals $\int P(y)f(y) dy$ and $\int \int P(y,z) f(y,z) dy dz$ are deduced. Using obtained identities, positivity of these expressions are characterized for higher order $\nabla-$convex and completely monotonic functions. Some applications in terms of generalized Cauchy means and exponential convexity are given.
UR - https://scma.maragheh.ac.ir/article_249585.html
L1 - https://scma.maragheh.ac.ir/article_249585_172a7aeb2e4fe6ea55ee687557aa2805.pdf
ER -