Generalized $ q $-convex functions characterized by $ q $-calculus-Reference-Cited by-同舟云学术

Generalized $ q $-convex functions characterized by $ q $-calculus

Published:2023 Issue:4 Volume:8 Page:9385-9399
ISSN:2473-6988
Container-title:AIMS Mathematics
language:
Short-container-title:MATH

Author:

Alqahtani Aisha M.¹,Murtaza Rashid²,Akmal Saba²,Adnan ²,Khan Ilyas³

Affiliation:

1. Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

2. Department of Mathematics, Mohi-Ud-Din Islamic University, Nerian Sharif, AJK, Pakistan

3. Department of Mathematics, College of Science, Al-Zulfi Majmaah University, Al-Majmaah 11952, Saudi Arabia

Abstract

<abstract><p>The objective of the current examination is to present new sub-classes of $ q $-convex and $ q $-starlike functions inside $ \mathcal E = \left\{z\in\mathbb C: \left|z\right| < 1\right\} $, by $ q $-difference operator. We determined connections of these classes and acquired a few fundamental properties, for instance, inclusion relation, subordination properties and $ q $-limits on real part.</p></abstract>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

General Mathematics

Reference14 articles.

1. P. L. Duren, Univalent functions, New York: Springer-Verlag, 1983.

2. A. W. Goodman, Univalent functions, Washington, New Jersey: Polygonal Publishing House, 1983.

3. M. E. H. Ismail, E. Merks, D. Styer, A generalization of starlike functions, Complex Var. Theory Appl., 14 (1990), 77–84. https://doi.org/10.1080/17476939008814407

4. F. H. Jackson, On $q$-functions and certain difference operators, Trans. Roy. Soc. Edinburgh, 46 (1909), 253–281. https://doi.org/10.1017/S0080456800002751

5. F. H. Jackson, On $q$-definite integrals, Quar. J. Pure Appl. Math., 41 (1910), 193–203.