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Abstract
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Article Information:
A Generalized Extension of the Hadamard-type Inequality for a Convex Function Defined on the Minimum Modulus of Integral Functions
Md Mainul Islam
Corresponding Author: Md Mainul Islam
Submitted: February 18, 2014
Accepted: May 08, 2014
Published: August 05, 2014 |
Abstract:
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In this study we extend the Hadamard’s type inequalities for convex functions defined on the minimum modulus 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 ln t (r) are continuous and convex in R+. Finally we derive two inequalities analogous to well known Hadamard’s inequality by using elementary analysis.
Key words: Analytic function, Hermite-Hadamard integral inequality, integral function, principal of maximum and minimum modulus, , , ,
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Cite this Reference:
Md Mainul Islam, . A Generalized Extension of the Hadamard-type Inequality for a Convex Function Defined on the Minimum Modulus of Integral Functions. Research Journal of Applied Sciences, Engineering and Technology, (5): 595-599.
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ISSN (Online): 2040-7467
ISSN (Print): 2040-7459 |
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