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Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, Number 2, Pages 11–23 (Mi basm529)  

Research articles

Inequalities of Hermite-Hadamard type for $K$-bounded modulus convex complex functions

Silvestru Sever Dragomir

College of Engineering & Science Victoria University, PO Box 14428 Melbourne City, MC 8001, Australia

Abstract: Let $D\subset \mathbb{C}$ be a convex domain of complex numbers and $K>0.$ We say that the function $f:D\subset \mathbb{C\rightarrow C}$ is called $K$-bounded modulus convex, for the given $K>0,$ if it satisfies the condition
\begin{equation*} \vert ( 1-\lambda ) f( x) +\lambda f( y) -f( ( 1-\lambda ) x+\lambda y) \vert \leq \frac{1}{2}K\lambda ( 1-\lambda ) \vert x-y\vert ^{2} \end{equation*}
for any $x,$ $y\in D$ and $\lambda \in [ 0,1] .$ In this paper we establish some new Hermite-Hadamard type inequalities for the complex integral on $\gamma ,$ a smooth path from $\mathbb{C}$, and $K$-bounded modulus convex functions. Some examples for integrals on segments and circular paths are also given.

Keywords and phrases: complex integral, continuous functions, holomorphic functions, hermite-Hadamard inequality, midpoint inequality, trapezoid inequality.

Full text: PDF file (137 kB)
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MSC: 26D15, 26D10, 30A10, 30A86
Received: 11.09.2019
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Citation: Silvestru Sever Dragomir, “Inequalities of Hermite-Hadamard type for $K$-bounded modulus convex complex functions”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2020, no. 2, 11–23

Citation in format AMSBIB
\Bibitem{Dra20}
\by Silvestru~Sever~Dragomir
\paper Inequalities of Hermite-Hadamard type for $K$-bounded modulus convex complex functions
\jour Bul. Acad. \c Stiin\c te Repub. Mold. Mat.
\yr 2020
\issue 2
\pages 11--23
\mathnet{http://mi.mathnet.ru/basm529}


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