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Some class of analytic functions related to conic domains

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Mathematica Slovaca

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 λ q f is defined. Applying R λ q f a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.

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Authors and Affiliations

  1. Institut of Mathematics, University of Rzeszów, Al. Rejtana 16, PL-35-959, Rzeszów, Poland

    Stanisława Kanas

  2. Department of Mathematics Faculty of Mathematics and Computer Science, Transilvania University of Braşov, 50091, Iuliu Maniu 50, Braşov, Romania

    Dorina Răducanu

Authors
  1. Stanisława Kanas
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  2. Dorina Răducanu
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Correspondence to Stanisława Kanas.

Additional information

Communicated by Ján Borsík

This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge, Faculty of Mathematics and Natural Sciences, University of Rzeszow.

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Kanas, S., Răducanu, D. Some class of analytic functions related to conic domains. Math. Slovaca 64, 1183–1196 (2014). https://doi.org/10.2478/s12175-014-0268-9

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