An Extension of the Hadamard-Type Inequality for a Convex Function Defined on Modulus of Complex Integral Functions

Md Mainul Islam, A.N.M. Rezaul Karim

Abstract


In this paper we extend the Hadamard's type inequalities for convex functions defined on the modulus of integral functions in complex field. Firstly, by using the Principal of maximum modulus theorem we show that $M(r)$ and $lnM(r)$ are continuous and convex functions for any non-negative values of $r$. Finally we derive two inequalities analogous to well known Hadamard's inequality by using elementary analysis.


Full Text: PDF DOI: 10.5539/jmr.v5n3p92

Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.

Journal of Mathematics Research   ISSN 1916-9795 (Print)   ISSN 1916-9809 (Online)

Copyright © Canadian Center of Science and Education

To make sure that you can receive messages from us, please add the 'ccsenet.org' domain to your e-mail 'safe list'. If you do not receive e-mail in your 'inbox', check your 'bulk mail' or 'junk mail' folders.