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16 pages, 277 KiB

Open AccessArticle

Initial Coefficient Bounds for Certain New Subclasses of Bi-Univalent Functions Involving Mittag–Leffler Function with Bounded Boundary Rotation

by Ibtisam Aldawish, Prathviraj Sharma, Sheza M. El-Deeb, Mariam R. Almutiri and Srikandan Sivasubramanian

Symmetry 2024, 16(8), 971; https://doi.org/10.3390/sym16080971 (registering DOI) - 31 Jul 2024

Abstract

By using the Mittag–Leffler function associated with functions of bounded boundary rotation, the authors introduce a few new subclasses of bi-univalent functions involving the Mittag–Leffler function with bounded boundary rotation in the open unit disk

D .

For these new classes, the authors [...] Read more.

By using the Mittag–Leffler function associated with functions of bounded boundary rotation, the authors introduce a few new subclasses of bi-univalent functions involving the Mittag–Leffler function with bounded boundary rotation in the open unit disk

D .

For these new classes, the authors establish initial coefficient bounds of

| a_{2} |

and

| a_{3} |

. Furthermore, the famous Fekete–Szegö coefficient inequality is also obtained for these new classes of functions. Full article

(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)

15 pages, 2401 KiB

Open AccessArticle

Some Properties and Graphical Applications of a New Subclass of Harmonic Functions Defined by a Differential Inequality

by Sibel Yalçın, Hasan Bayram and Georgia Irina Oros

Mathematics 2024, 12(15), 2338; https://doi.org/10.3390/math12152338 - 26 Jul 2024

Viewed by 263

Abstract

This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of [...] Read more.

This paper establishes new results related to geometric function theory by presenting a new subclass of harmonic functions with complex values within the open unit disk, characterized by a second-order differential inequality. The investigation explores the bounds on the coefficients and estimates of the function growth. This paper also demonstrates that this subclass remains stable under the convolution operation applied to its members. In addition, in the last section, images of the unit disk under some functions of this class are given. Full article

(This article belongs to the Special Issue Advances in Complex Analysis and Application)

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12 pages, 326 KiB

Open AccessArticle

Fuzzy Differential Subordination for Classes of Admissible Functions Defined by a Class of Operators

by Ekram E. Ali, Miguel Vivas-Cortez and Rabha M. El-Ashwah

Fractal Fract. 2024, 8(7), 405; https://doi.org/10.3390/fractalfract8070405 - 11 Jul 2024

Viewed by 426

Abstract

This paper’s findings are related to geometric function theory (GFT). We employ one of the most recent methods in this area, the fuzzy admissible functions methodology, which is based on fuzzy differential subordination, to produce them. To do this, the relevant fuzzy admissible [...] Read more.

This paper’s findings are related to geometric function theory (GFT). We employ one of the most recent methods in this area, the fuzzy admissible functions methodology, which is based on fuzzy differential subordination, to produce them. To do this, the relevant fuzzy admissible function classes must first be defined. This work deals with fuzzy differential subordinations, ideas borrowed from fuzzy set theory and applied to complex analysis. This work examines the characteristics of analytic functions and presents a class of operators in the open unit disk

J_{η, ς}^{κ} (a, e, x)

for

ς > - 1, η > 0,

such that

a, e \in R, (e - a) \geq 0, a > - x

. The fuzzy differential subordination results are obtained using (GFT) concepts outside the field of complex analysis because of the operator’s compositional structure, and some relevant classes of admissible functions are studied by utilizing fuzzy differential subordination. Full article

(This article belongs to the Special Issue Fractional Integral Inequalities and Applications, 2nd Edition)

16 pages, 331 KiB

Open AccessArticle

Some Classes of Bazilevič-Type Close-to-Convex Functions Involving a New Derivative Operator

by Pishtiwan Othman Sabir, Alina Alb Lupas, Sipal Saeed Khalil, Pshtiwan Othman Mohammed and Mohamed Abdelwahed

Symmetry 2024, 16(7), 836; https://doi.org/10.3390/sym16070836 - 3 Jul 2024

Viewed by 651

Abstract

In the present paper, we are merging two interesting and well-known classes, namely those of Bazilevič and close-to-convex functions associated with a new derivative operator. We derive coefficient estimates for this broad category of analytic, univalent and bi-univalent functions and draw attention to [...] Read more.

In the present paper, we are merging two interesting and well-known classes, namely those of Bazilevič and close-to-convex functions associated with a new derivative operator. We derive coefficient estimates for this broad category of analytic, univalent and bi-univalent functions and draw attention to the Fekete–Szegö inequalities relevant to functions defined within the open unit disk. Additionally, we identify several specific special cases of our results by specializing the parameters. Full article

(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)

23 pages, 360 KiB

Open AccessArticle

Sharp Coefficient Bounds for Starlike Functions Associated with Cosine Function

by Rashid Ali, Mohsan Raza and Teodor Bulboacă

Axioms 2024, 13(7), 442; https://doi.org/10.3390/axioms13070442 - 29 Jun 2024

Viewed by 407

Abstract

Let

S_{cos}^{*}

denote the class of normalized analytic functions f in the open unit disk

D

satisfying the subordination

\frac{z f^{'} (z)}{f (z)} ≺ cos z

. In the first result of this article, we [...] Read more.

Let

S_{cos}^{*}

denote the class of normalized analytic functions f in the open unit disk

D

satisfying the subordination

\frac{z f^{'} (z)}{f (z)} ≺ cos z

. In the first result of this article, we find the sharp upper bounds for the initial coefficients

a_{3}

,

a_{4}

and

a_{5}

and the sharp upper bound for module of the Hankel determinant

| H_{2, 3} (f) |

for the functions from the class

S_{cos}^{*}

. The next section deals with the sharp upper bounds of the logarithmic coefficients

γ_{3}

and

γ_{4}

. Then, in addition, we found the sharp upper bound for

|H_{2, 2} (F_{f} / 2)|

. To obtain these results we utilized the very useful and appropriate Lemma 2.4 of N.E. Cho et al., which gave a most accurate description for the first five coefficients of the functions from the Carathéodory’s functions class, and provided a technique for finding the maximum value of a three-variable function on a closed cuboid. All the maximum found values were checked by using MAPLE™ computer software, and we also found the extremal functions in each case. All of our most recent results are the best ones and give sharp versions of those recently published by Hacet. Full article

(This article belongs to the Special Issue Recent Advances in Complex Analysis and Related Topics)

13 pages, 1417 KiB

Open AccessArticle

A Bi-Starlike Class in a Leaf-like Domain Defined through Subordination via

q ̧

-Calculus

by Ala Amourah, Abdullah Alsoboh, Daniel Breaz and Sheza M. El-Deeb

Mathematics 2024, 12(11), 1735; https://doi.org/10.3390/math12111735 - 3 Jun 2024

Viewed by 383

Abstract

Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with

q

-calculus. [...] Read more.

Bi-univalent functions associated with the leaf-like domain within the open unit disk are investigated and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with

q

-calculus. The class is proved to be not empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on

| α_{2} |

and

| α_{3} |

coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. Full article

(This article belongs to the Special Issue Advances in Complex Analysis and Application)

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15 pages, 659 KiB

Open AccessArticle

A Class of Bi-Univalent Functions in a Leaf-Like Domain Defined through Subordination via

q ̧

-Calculus

by Abdullah Alsoboh and Georgia Irina Oros

Mathematics 2024, 12(10), 1594; https://doi.org/10.3390/math12101594 - 20 May 2024

Cited by 3 | Viewed by 537

Abstract

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with

q

-calculus. The [...] Read more.

Bi-univalent functions associated with the leaf-like domain within open unit disks are investigated, and a new subclass is introduced and studied in the research presented here. This is achieved by applying the subordination principle for analytic functions in conjunction with

q

-calculus. The class is proved to not be empty. By proving its existence, generalizations can be given to other sets of functions. In addition, coefficient bounds are examined with a particular focus on

| α_{2} |

and

| α_{3} |

coefficients, and Fekete–Szegö inequalities are estimated for the functions in this new class. To support the conclusions, previous works are cited for confirmation. Full article

(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)

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15 pages, 334 KiB

Open AccessArticle

Initial Coefficient Bounds Analysis for Novel Subclasses of Bi-Univalent Functions Linked with Lucas-Balancing Polynomials

by Sondekola Rudra Swamy, Daniel Breaz, Kala Venugopal, Mamatha Paduvalapattana Kempegowda, Luminita-Ioana Cotîrlă and Eleonora Rapeanu

Mathematics 2024, 12(9), 1325; https://doi.org/10.3390/math12091325 - 26 Apr 2024

Viewed by 493

Abstract

We investigate some subclasses of regular and bi-univalent functions in the open unit disk that are associated with Lucas-Balancing polynomials in this work. For functions that belong to these subclasses, we obtain upper bounds on their initial coefficients. The Fekete–Szegö problem is also [...] Read more.

We investigate some subclasses of regular and bi-univalent functions in the open unit disk that are associated with Lucas-Balancing polynomials in this work. For functions that belong to these subclasses, we obtain upper bounds on their initial coefficients. The Fekete–Szegö problem is also discussed. Along with presenting some new results, we also explore pertinent connections to earlier findings. Full article

10 pages, 260 KiB

Open AccessArticle

On α-Pseudo Spiralike Functions Associated with Exponential Pareto Distribution (EPD) and Libera Integral Operator

by Jamiu Olusegun Hamzat, Matthew Olanrewaju Oluwayemi, Abiodun Tinuoye Oladipo and Alina Alb Lupas

Mathematics 2024, 12(9), 1305; https://doi.org/10.3390/math12091305 - 25 Apr 2024

Viewed by 516

Abstract

The present study aims at investigating some characterizations of a new subclass

G_{α} (μ, τ)

and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a [...] Read more.

The present study aims at investigating some characterizations of a new subclass

G_{α} (μ, τ)

and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a compound function

L_{x, n}^{σ} (z)

is derived from the convolution of the analytic function

f (z)

and a modified exponential Pareto distribution

G (x)

in conjunction with the famous Libera integral operator

L (ζ)

. With the aid of the derived function, the aforementioned subclass

G_{α} (μ, τ)

is introduced, while some properties of functions belonging to this subclass are considered in the open unit disk. Full article

(This article belongs to the Special Issue New Trends in Complex Analysis Research, 2nd Edition)

10 pages, 1511 KiB

Open AccessArticle

On Third Hankel Determinant for Certain Subclass of Bi-Univalent Functions

by Qasim Ali Shakir and Waggas Galib Atshan

Symmetry 2024, 16(2), 239; https://doi.org/10.3390/sym16020239 - 16 Feb 2024

Cited by 3 | Viewed by 743

Abstract

This study presents a subclass

S (β)

of bi-univalent functions within the open unit disk region

D

. The objective of this class is to determine the bounds of the Hankel determinant of order 3, (

Ⱨ_{3} (1)

[...] Read more.

This study presents a subclass

S (β)

of bi-univalent functions within the open unit disk region

D

. The objective of this class is to determine the bounds of the Hankel determinant of order 3, (

Ⱨ_{3} (1)

). In this study, new constraints for the estimates of the third Hankel determinant for the class

S (β)

are presented, which are of considerable interest in various fields of mathematics, including complex analysis and geometric function theory. Here, we define these bi-univalent functions as

S (β)

and impose constraints on the coefficients

{│ a}_{n} │

. Our investigation provides the upper bounds for the bi-univalent functions in this newly developed subclass, specifically for n = 2, 3, 4, and 5. We then derive the third Hankel determinant for this particular class, which reveals several intriguing scenarios. These findings contribute to the broader understanding of bi-univalent functions and their potential applications in diverse mathematical contexts. Notably, the results obtained may serve as a foundation for future investigations into the properties and applications of bi-univalent functions and their subclasses. Full article

(This article belongs to the Special Issue Geometric Function Theory and Special Functions II)

13 pages, 290 KiB

Open AccessArticle

Bi-Concave Functions Connected with the Combination of the Binomial Series and the Confluent Hypergeometric Function

by Hari M. Srivastava, Sheza M. El-Deeb, Daniel Breaz, Luminita-Ioana Cotîrlă and Grigore Stefan Sălăgean

Symmetry 2024, 16(2), 226; https://doi.org/10.3390/sym16020226 - 13 Feb 2024

Viewed by 696

Abstract

In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the [...] Read more.

In this article, we first define and then propose to systematically study some new subclasses of the class of analytic and bi-concave functions in the open unit disk. For this purpose, we make use of a combination of the binomial series and the confluent hypergeometric function. Among some other properties and results, we derive the estimates on the initial Taylor-Maclaurin coefficients

| a_{2} |

and

| a_{3} |

for functions in these analytic and bi-concave function classes, which are introduced in this paper. We also derive a number of corollaries and consequences of our main results in this paper. Full article

(This article belongs to the Section Mathematics)

12 pages, 1815 KiB

Open AccessArticle

Certain Results on Subclasses of Analytic and Bi-Univalent Functions Associated with Coefficient Estimates and Quasi-Subordination

by Elaf Ibrahim Badiwi, Waggas Galib Atshan, Ameera N. Alkiffai and Alina Alb Lupas

Symmetry 2023, 15(12), 2208; https://doi.org/10.3390/sym15122208 - 17 Dec 2023

Viewed by 1067

Abstract

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi-univalent functions defined in open unit disks connected with a linear q-convolution operator, which are associated with quasi-subordination. We find coefficient estimates of [...] Read more.

The purpose of the present paper is to introduce and investigate new subclasses of analytic function class of bi-univalent functions defined in open unit disks connected with a linear q-convolution operator, which are associated with quasi-subordination. We find coefficient estimates of

|h_{2}|, |h_{3}|

for functions in these subclasses. Several known and new consequences of these results are also pointed out. There is symmetry between the results of the subclass

f_{q, \sum}^{μ} (ζ, n, ρ, σ, ϑ, γ, δ, φ)

and the results of the subclass

ℵ_{\sum}^{q, δ} (λ, ζ, n, ρ, σ, ϑ, φ)

. Full article

(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)

21 pages, 316 KiB

Open AccessArticle

Multiplication Operators on Weighted Zygmund Spaces of the First Cartan Domain

by Zhi-Jie Jiang

Axioms 2023, 12(12), 1131; https://doi.org/10.3390/axioms12121131 - 17 Dec 2023

Cited by 1 | Viewed by 980

Abstract

Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that [...] Read more.

Inspired by some recent studies of the multiplication operators on holomorphic function spaces of the classical domains such as the open unit disk, the unit ball and the unit polydisk, the purpose of the present paper is to study just the operators that are defined on weighted Zygmund spaces of the first Cartan domain. We obtain some necessary conditions and sufficient conditions for the operators to be bounded and compact. Full article

(This article belongs to the Special Issue Recent Advances in Functional Analysis and Operator Theory)

16 pages, 329 KiB

Open AccessArticle

Faber Polynomial Coefficient Inequalities for a Subclass of Bi-Close-To-Convex Functions Associated with Fractional Differential Operator

by Ferdous M. O. Tawfiq, Fairouz Tchier and Luminita-Ioana Cotîrlă

Fractal Fract. 2023, 7(12), 883; https://doi.org/10.3390/fractalfract7120883 - 14 Dec 2023

Viewed by 926

Abstract

In this study, we begin by examining the

τ

-fractional differintegral operator and proceed to establish a novel subclass in the open unit disk E. The determination of the nth coefficient bound for functions within this recently established class is accomplished [...] Read more.

In this study, we begin by examining the

τ

-fractional differintegral operator and proceed to establish a novel subclass in the open unit disk E. The determination of the nth coefficient bound for functions within this recently established class is accomplished by the use of the Faber polynomial expansion approach. Additionally, we examine the behavior of the initial coefficients of bi-close-to-convex functions defined by the

τ

-fractional differintegral operator, which may exhibit unexpected reactions. We established connections between our current research and prior studies in order to validate our significant findings. Full article

(This article belongs to the Section General Mathematics, Analysis)

13 pages, 307 KiB

Open AccessArticle

Sharp Estimates Involving a Generalized Symmetric Sălăgean q-Differential Operator for Harmonic Functions via Quantum Calculus

by Isra Al-Shbeil, Shahid Khan, Fairouz Tchier, Ferdous M. O. Tawfiq, Amani Shatarah and Adriana Cătaş

Symmetry 2023, 15(12), 2156; https://doi.org/10.3390/sym15122156 - 4 Dec 2023

Cited by 1 | Viewed by 760

Abstract

In this study, we apply q-symmetric calculus operator theory and investigate a generalized symmetric Sălăgean q-differential operator for harmonic functions in an open unit disk. We consider a newly defined operator and establish new subclasses of harmonic functions in complex order. [...] Read more.

In this study, we apply q-symmetric calculus operator theory and investigate a generalized symmetric Sălăgean q-differential operator for harmonic functions in an open unit disk. We consider a newly defined operator and establish new subclasses of harmonic functions in complex order. We determine the sharp results, such as the sufficient necessary coefficient bounds, the extreme of closed convex hulls, and the distortion theorems for a new family of harmonic functions. Further, we illustrate how we connect the findings of previous studies and the results of this article. Full article

(This article belongs to the Special Issue Selected Papers from International Symposium on Geometric Function Theory and Applications (GFTA))

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