A note on convolution of Janowski type functions with q-derivative

F. Alsarari

doi:10.2478/ausm-2023-0001

.blurhash-client-img { display: none !important; }

A note on convolution of Janowski type functions with q-derivative

Acta Universitatis Sapientiae, Mathematica

Volume 15 (2023): Issue 1 (November 2023)

By: F. Alsarari

Open Access

|Nov 2023

Abstract

The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with q-derivative. We also study certain a convolution conditions, and apply the convolution conditions to get sufficient condition and the neighborhood results related to the functions in the class 𝒮_q(A, B, α).

References

P. L. Duren, Univalent Functions, Springer-Verlag, (1983).
Search in Google Scholar Back to article
W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math. 28 (3), (1973), 297–326.
Search in Google Scholar Back to article
Y. Polatoglu, M. Bolcal, A. Sen and E. Yavuz, A study on the generalization of Janowski functions in the unit disc, Acta Math. Acad. Paedag. Nyhazi.22, (2006), 27–31.
Search in Google Scholar Back to article
F. H. Jackson, On q-functions and a certain difference operator, Trans. Royal Soc. Edinb, 46, (1909), 253-281.
Search in Google Scholar Back to article
A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8, (1957), 598–601.
Search in Google Scholar Back to article
S. Ruschewyh, Neighborhoods of univalent functions, Proc. Amer.Math. Soc. 81, (1981), 521–527.
Search in Google Scholar Back to article
M. S. Ganesan, and K. S. Padmanabhan, Convolution conditions for certain classes of analytic functions, Int. J. Pure and Appl. Math. 15(7), (1984), 777–780.
Search in Google Scholar Back to article
H. Silverman, E. M. Silvia and D. Telage, Convolution conditions for convexity, starlikeness and spiral-likeness, Math. Z, 162(2), (1978), 125–130.
Search in Google Scholar Back to article

DOI: https://doi.org/10.2478/ausm-2023-0001 | Journal eISSN: 2066-7752

Journal RSS Feed

Language: English

Page range: 1 - 11

Submitted on: Jul 22, 2020

Published on: Nov 15, 2023

Published by: Sapientia Hungarian University of Transylvania

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

convolution or Hadamard product

Related subjects:

Mathematics,

General mathematics

© 2023 F. Alsarari, published by Sapientia Hungarian University of Transylvania
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 15 (2023): Issue 1 (November 2023)Next article