학술논문
On Sapogov's extension of Čebyšev's inequality and related results.
Document Type
Journal
Author
Adil Khan, M. (PAK-GCU-SM) AMS Author Profile; Latif, Naveed (PAK-GCUF-M) AMS Author Profile; Pečarić, J. (CT-ZAGRTX) AMS Author Profile; Perić, I. (CT-ZAGRFB) AMS Author Profile
Source
Subject
28 Measure and integration -- 28A Classical measure theory
28A15Abstract differentiation theory, differentiation of set functions
90Operations research, mathematical programming -- 90C Mathematical programming
90C25Convex programming
28A15
90
90C25
Language
English
Abstract
In this paper Sapogov's extension of Chebyshev's inequality is given. Jointly with convex functions and a Green function, it is used to prove a majorization inequality for double integrals. Furthermore, for these inequalities two mean value theorems are given, and some important applications of generalized Cauchy means are also presented.