(k1, …, kn)-CONVEXITY IN ℝn

PARK, SUNG-HEE

• Accepted : 2015.12.01
• Published : 2015.12.25
• 27 1

Abstract

In this paper, we first introduce and study new concepts of ($k_1,{\cdots},k_n$)-convexity and k-segment. Secondly, we shall discuss some properties of nonisotropically starlike domains in $\mathbb{R}^n$ with respect to the origin.

Keywords

($k_1,{\cdots},k_n$)-convex set;($k_1,{\cdots},k_n$)-convex function;quasi-($k_1,{\cdots},k_n$)-convex function;k-segment;($k_1,{\cdots},k_n$)-nonisotropically starlike with respect to the origin

References

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2. W. Fleming, Functions of Several Variables, 2nd ed., Undergraduate Texts in Mathematics, Springer, New York/Heidelberg, 1977.
3. M. Jarnicki & P. Pflug, Invariant Distances and Metrics in Complex Analysis, 2nd Extended ed., de Gruyter Expositions in Mathematics 9, Walter de Gruyter, 2013.