Some class of analytic functions related to conic domains

By Stanislawa Kanas, Dorina Raducanu. 2014

262 citations recorded by the source corpus.

AbstractFor 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 Rqλf is defined. Applying Rqλf a subfamily of analytic functions is defined. Several interesting properties of a defined family of functions are investigated.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/7e0feb330c87149452f157b534f9ee663506c72e

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Some Applications of a New Integral Operator in q-Analog for Multivalent Functions (2019, methodology): “[13] used Hadamad product to define the q-extension of the Ruscheweyh operator.”
On a class of analytic functions related to conic domains involving q-calculus (2017, methodology): “Note that as q → 1−, the class Sq(k, 0,m) reduces to the class T (k,m) investigated by Kanas and Yaguchi [15] and the class Sq(k, α, 0) reduces to the class ST (k, α) investigated by Kanas and Răducanu [17] respectively.”
Study on the q-analogue of a certain family of linear operators (2019, unknown): “In [15], the authors introduced the q-analogue of the Ruscheweyh derivative operator and studied some of the properties of this differential operator.”
New Subclass of Analytic Functions in Conical Domain Associated with Ruscheweyh q-Differential Operator (2017, background): “When A = 1 − 2α, B = −1, β = 0 with 0 ≤ α < 1, then we have the following known result, proved by Kanas and Raducanu in [7].”
A Subfamily of Univalent Functions Associated with -Analogue of Noor Integral Operator (2018, methodology): “Using convolution of normalized analytic functions, Kanas and Raducanu [7] defined q-analogue of Ruscheweyh differential operator and studied some of its properties.”