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


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.

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

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