Research Article | OPEN ACCESS
A Generalized Extension of the Hadamard-type Inequality for a Convex Function Defined on the Minimum Modulus of Integral Functions
Md Mainul Islam
Department of Mathematics and Statistics, Bangladesh University of Business and
Technology, Bangladesh
Research Journal of Applied Sciences, Engineering and Technology 2014 5:595-599
Received: February 18, 2014 | Accepted: May ‎08, ‎2014 | Published: August 05, 2014
Abstract
In this study we extend the Hadamard’s type inequalities for convex functions defined on the minimummodulus of integral functions in complex field. Firstly, using the Principal of minimum modulus theorem we derive that m (r) is continuous and decreasing function in R+. Secondly, we introduce a function t (r) and derived that t (r) and lnt (r) are continuous and convex in R+. Finally we derive two inequalities analogous to well known Hadamard’s inequality by using elementary analysis.
Keywords:
Analytic function, Hermite-Hadamard integral inequality , integral function , principal of maximum and minimum modulus,
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Competing interests
The authors have no competing interests.
Open Access Policy
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Copyright
The authors have no competing interests.
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