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,

References

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Competing interests

The authors have no competing interests.

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The authors have no competing interests.