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

Aisha M. Alqahtani; Rashid Murtaza; Saba Akmal; Adnan; Ilyas Khan; Aisha M. Alqahtani; Rashid Murtaza; Saba Akmal; Adnan; Ilyas Khan

doi:10.3934/math.2023472

AIMS Mathematics

2023, Volume 8, Issue 4: 9385-9399. doi: 10.3934/math.2023472

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

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

Received: 22 January 2022 Revised: 27 April 2022 Accepted: 24 May 2022 Published: 15 February 2023
MSC : 30C45, 30C10

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.
- analytic functions,
- second-order $ q $-differential,
- convolution,
- subordination,
- $ q $-number
Citation: Aisha M. Alqahtani, Rashid Murtaza, Saba Akmal, Adnan, Ilyas Khan. Generalized $ q $-convex functions characterized by $ q $-calculus[J]. AIMS Mathematics, 2023, 8(4): 9385-9399. doi: 10.3934/math.2023472

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Abstract

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.

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