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SOME REMARKS ON FUNCTIONS WITH NON-DECREASING INCREMENTS.

Authors :
KHAN, ASIF RAZA
MEHMOOD, FARAZ
Source :
Journal of Mathematical Analysis. 2020, Vol. 11 Issue 1, p1-16. 16p.
Publication Year :
2020

Abstract

The main purpose of this work is to establish relationship of functions with non-decreasing increments with other functions of high importance. Especially, we pay attention to the role of representation and connection among functions with non-decreasing increments and arithmetic integral mean, Wright convex functions, convex functions, ∇−convex functions, Jensen m−connvex functions, m−convex functions, m−∇−convex functions, k−monotonic functions, absolutely monotonic functions, completely monotonic functions, Laplace Transform and exponentially convex functions, by using the method of finite difference operator as different cases of ∆m h f(y). We also consider function with non-decreasing increments of order three and obtain the generalisation of the Levinson’s-type inequality and Jensen-Mercer’s-type inequality by using Jensen-Boas inequality and also deduce some results. [ABSTRACT FROM AUTHOR]

Details

Language :
English
ISSN :
21173419
Volume :
11
Issue :
1
Database :
Academic Search Index
Journal :
Journal of Mathematical Analysis
Publication Type :
Academic Journal
Accession number :
141087851