Research

11 pages, 336 KiB

Open AccessArticle

Certain Class of Bi-Univalent Functions Defined by Sălăgean q-Difference Operator Related with Involution Numbers

by Daniel Breaz, Gangadharan Murugusundaramoorthy, Kaliappan Vijaya and Luminiţa-Ioana Cotîrlǎ

Symmetry 2023, 15(7), 1302; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15071302 - 23 Jun 2023

Cited by 4 | Viewed by 940

We introduce and examine two new subclass of bi-univalent function

Σ,

defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients

| a_{2} |

[...] Read more.

We introduce and examine two new subclass of bi-univalent function

Σ,

defined in the open unit disk, based on Sălăgean-type q-difference operators which are subordinate to the involution numbers. We find initial estimates of the Taylor–Maclaurin coefficients

| a_{2} |

and

| a_{3} |

for functions in the new subclass introduced here. We also obtain a Fekete–Szegö inequality for the new function class. Several new consequences of our results are pointed out, which are new and not yet discussed in association with involution numbers. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

15 pages, 322 KiB

Open AccessArticle

Certain Subclasses of Analytic and Bi-Univalent Functions Governed by the Gegenbauer Polynomials Linked with q-Derivative

by Sercan Kazımoğlu, Erhan Deniz and Luminiţa-Ioana Cotîrlă

Symmetry 2023, 15(6), 1192; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15061192 - 02 Jun 2023

Cited by 2 | Viewed by 906

Abstract

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions using the q-derivative operator

D_{q} (0 < q < 1)

and the Gegenbauer polynomials in a symmetric domain, which is the open unit disc [...] Read more.

In this paper, we introduce and investigate two new subclasses of analytic and bi-univalent functions using the q-derivative operator

D_{q} (0 < q < 1)

and the Gegenbauer polynomials in a symmetric domain, which is the open unit disc

Λ = \{℘ : ℘ \in C and |℘| < 1\} .

For these subclasses of analytic and bi-univalent functions, the coefficient estimates and Fekete–Szegö inequalities are solved. Some special cases of the main results are also linked to those in several previous studies. The symmetric nature of quantum calculus itself motivates our investigation of the applications of such quantum (or q-) extensions in this paper. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

14 pages, 314 KiB

Open AccessArticle

Investigating New Subclasses of Bi-Univalent Functions Associated with q-Pascal Distribution Series Using the Subordination Principle

by Abdullah Alsoboh, Ala Amourah, Maslina Darus and Carla Amoi Rudder

Symmetry 2023, 15(5), 1109; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15051109 - 18 May 2023

Cited by 5 | Viewed by 883

Abstract

In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of [...] Read more.

In the real world, there are many applications that find the Pascal distribution to be a useful and relevant model. One of these is the normal distribution. In this work, we develop a new subclass of analytic bi-univalent functions by making use of the q-Pascal distribution series as a construction. These functions involve the q-Gegenbauer polynomials, and we use them to establish our new subclass. Moreover, we solve the Fekete–Szegö functional problem and analyze various different estimates of the Maclaurin coefficients for functions that belong to the new subclass. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

12 pages, 302 KiB

Open AccessArticle

On a Subfamily of q-Starlike Functions with Respect to m-Symmetric Points Associated with the q-Janowski Function

by Ihtesham Gul, Sa’ud Al-Sa’di, Khalida Inayat Noor and Saqib Hussain

Symmetry 2023, 15(3), 652; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15030652 - 05 Mar 2023

Cited by 1 | Viewed by 957

Abstract

The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego [...] Read more.

The main objective of this paper is to study a new family of analytic functions that are q-starlike with respect to m-symmetrical points and subordinate to the q-Janowski function. We investigate inclusion results, sufficient conditions, coefficients estimates, bounds for Fekete–Szego functional

| a_{3} - μ a_{2}^{2} |

and convolution properties for the functions belonging to this new class. Several consequences of main results are also obtained. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

9 pages, 292 KiB

Open AccessArticle

A Family of Analytic and Bi-Univalent Functions Associated with Srivastava-Attiya Operator

by Adel A. Attiya and Mansour F. Yassen

Symmetry 2022, 14(10), 2006; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14102006 - 25 Sep 2022

Cited by 2 | Viewed by 961

Abstract

In this paper, we investigate a new family of normalized analytic functions and bi-univalent functions associated with the Srivastava–Attiya operator. We use the Faber polynomial expansion to estimate the bounds for the general coefficients

| a_{n} |

of this family. The bounds [...] Read more.

In this paper, we investigate a new family of normalized analytic functions and bi-univalent functions associated with the Srivastava–Attiya operator. We use the Faber polynomial expansion to estimate the bounds for the general coefficients

| a_{n} |

of this family. The bounds values for the initial Taylor–Maclaurin coefficients of the functions in this family are also established. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

9 pages, 285 KiB

Open AccessArticle

Fekete–Szegö Inequalities for a New Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials

by Murat Çağlar, Luminiţa-Ioana Cotîrlă and Mucahit Buyankara

Symmetry 2022, 14(8), 1572; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081572 - 30 Jul 2022

Cited by 12 | Viewed by 1136

Abstract

We introduce and investigate in this paper a new subclass of bi-univalent functions associated with the Gegenbauer polynomials which satisfy subordination conditions defined in a symmetric domain, which is the open unit disc. For this new subclass, we obtain estimates for the Taylor–Maclaurin [...] Read more.

We introduce and investigate in this paper a new subclass of bi-univalent functions associated with the Gegenbauer polynomials which satisfy subordination conditions defined in a symmetric domain, which is the open unit disc. For this new subclass, we obtain estimates for the Taylor–Maclaurin coefficients

|a_{2}|,

|a_{3}|

and the Fekete–Szegö inequality

|a_{3} - μ a_{2}^{2}| .

Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

13 pages, 331 KiB

Open AccessArticle

A Differential Operator Associated with q-Raina Function

by Adel A. Attiya, Rabha W. Ibrahim, Abeer M. Albalahi, Ekram E. Ali and Teodor Bulboacă

Symmetry 2022, 14(8), 1518; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081518 - 25 Jul 2022

Cited by 6 | Viewed by 1266

Abstract

The topics studied in the geometric function theory of one variable functions are connected with the concept of Symmetry because for some special cases the analytic functions map the open unit disk onto a symmetric domain. Thus, if all the coefficients of the [...] Read more.

The topics studied in the geometric function theory of one variable functions are connected with the concept of Symmetry because for some special cases the analytic functions map the open unit disk onto a symmetric domain. Thus, if all the coefficients of the Taylor expansion at the origin are real numbers, then the image of the open unit disk is a symmetric domain with respect to the real axis. In this paper, we formulate the q-differential operator associated with the q-Raina function using quantum calculus, that is the so-called Jacksons’ calculus. We establish a new subclass of analytic functions in the unit disk by using this newly developed operator. The theory of differential subordination inspired our approach; therefore, we geometrically explore the most popular properties of this new operator: subordination properties, coefficient bounds, and the Fekete-Szegő problem. As special cases, we highlight certain well-known corollaries of our primary findings. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

20 pages, 308 KiB

Open AccessArticle

Some Inclusion Relations of Certain Subclasses of Strongly Starlike, Convex and Close-to-Convex Functions Associated with a Pascal Operator

by Abdel Moneim Y. Lashin, Mohamed K. Aouf, Abeer O. Badghaish and Amani Z. Bajamal

Symmetry 2022, 14(6), 1079; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14061079 - 24 May 2022

Cited by 2 | Viewed by 1155

Abstract

This paper studies some inclusion properties of some new subclasses of analytic functions in the open symmetric unit disc U that are associated with the Pascal operator. Furthermore, the integral-preserving properties in a sector for these subclasses are also investigated. Full article

(This article belongs to the Special Issue Symmetry in Geometric Function Theory)

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