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Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia


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Volume 64, Issue 5

Issues

Some class of analytic functions related to conic domains

Stanisława Kanas / Dorina Răducanu
  • Department of Mathematics Faculty of Mathematics and Computer Science, Transilvania University of Braşov, 50091, Iuliu Maniu 50, Braşov, Romania
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Published Online: 2014-11-15 | DOI: https://doi.org/10.2478/s12175-014-0268-9

Abstract

For q ∈ (0, 1) let the q-difference operator be defined as follows $$\partial _q f(z) = \frac{{f(qz) - f(z)}} {{z(q - 1)}} (z \in \mathbb{U}),$$ where $$\mathbb{U}$$ denotes the open unit disk in a complex plane. Making use of the above operator the extended Ruscheweyh differential operator R qλ f is defined. Applying R qλ f a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.

MSC: Primary 30C45; Secondary 30F60

Keywords: analytic functions; starlike; convex; uniformly convex functions; q-derivative operator; conic sections

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About the article

Published Online: 2014-11-15

Published in Print: 2014-10-01


Citation Information: Mathematica Slovaca, Volume 64, Issue 5, Pages 1183–1196, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-014-0268-9.

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© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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