Mathematics

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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 651

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, 249 KiB

Open AccessArticle

On Meromorphic Parabolic Starlike Functions with Fixed Point Involving the q-Hypergeometric Function and Fixed Second Coefficients

by Norah Saud Almutairi, Awatef Shahen and Hanan Darwish

Mathematics 2023, 11(13), 2991; https://doi.org/10.3390/math11132991 - 4 Jul 2023

Viewed by 876

Abstract

This article defines a new class of meromorphic parabolic starlike functions in the punctured unit disc

D^{*} = {z \in C : 0 < | z | < 1}

that includes fixed second coefficients of class [...] Read more.

This article defines a new class of meromorphic parabolic starlike functions in the punctured unit disc

D^{*} = {z \in C : 0 < | z | < 1}

that includes fixed second coefficients of class

A_{s, c}^{d} (ψ, τ, ν, η)

and the q- hypergeometric functions. For the function belonging to the class

A_{s, c}^{d} (ψ, τ, ν, η),

some properties are obtained, including the coefficient inequalities, closure theorems, and the radius of convexity. Full article

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

14 pages, 297 KiB

Open AccessArticle

Some Further Coefficient Bounds on a New Subclass of Analytic Functions

by Yue-Juan Sun, Muhammad Arif, Lei Shi and Muhammad Imran Faisal

Mathematics 2023, 11(12), 2784; https://doi.org/10.3390/math11122784 - 20 Jun 2023

Viewed by 980

Abstract

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass

SQ

of analytic functions with

f^{'} (z)

subordinated to

1 / {(1 - z)}^{2}

[...] Read more.

The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass

SQ

of analytic functions with

f^{'} (z)

subordinated to

1 / {(1 - z)}^{2}

in the open unit disk. This class was introduced and studied by Răducanu. Our main aim is to give the sharp upper bounds of the second Hankel determinant

H_{2, 3} (f)

and the third Hankel determinant

H_{3, 1} (f)

for

f \in SQ

. This may help to understand more properties of functions in this class and inspire further investigations on higher Hankel determinants for this or other popular sub-classes of univalent functions. Full article

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

19 pages, 384 KiB

Open AccessArticle

Subclasses of p-Valent κ-Uniformly Convex and Starlike Functions Defined by the q-Derivative Operator

by Ekram E. Ali, Hari M. Srivastava and Abeer M. Albalahi

Mathematics 2023, 11(11), 2578; https://doi.org/10.3390/math11112578 - 4 Jun 2023

Cited by 6 | Viewed by 1271

Abstract

The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are [...] Read more.

The potential for widespread applications of the geometric and mapping properties of functions of a complex variable has motivated this article. On the other hand, the basic or quantum (or q-) derivatives and the basic or quantum (or q-) integrals are extensively applied in many different areas of the mathematical, physical and engineering sciences. Here, in this article, we first apply the q-calculus in order to introduce the q-derivative operator

S_{η, p, q}^{n, m}

. Secondly, by means of this q-derivative operator, we define an interesting subclass

T ℵ_{λ, p}^{n, m} (η, α, κ)

of the class of normalized analytic and multivalent (or p-valent) functions in the open unit disk

U

. This p-valent analytic function class is associated with the class

κ

-

UCV

of

κ

-uniformly convex functions and the class

κ

-

UST

of

κ

-uniformly starlike functions in

U

. For functions belonging to the normalized analytic and multivalent (or p-valent) function class

T ℵ_{λ, p}^{n, m} (η, α, κ)

, we then investigate such properties as those involving (for example) the coefficient bounds, distortion results, convex linear combinations, and the radii of starlikeness, convexity and close-to-convexity. We also consider a number of corollaries and consequences of the main findings, which we derived herein. Full article

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

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12 pages, 324 KiB

Open AccessArticle

Some Properties of Certain Multivalent Harmonic Functions

by Georgia Irina Oros, Sibel Yalçın and Hasan Bayram

Mathematics 2023, 11(11), 2416; https://doi.org/10.3390/math11112416 - 23 May 2023

Cited by 4 | Viewed by 1288

Abstract

In this paper, various features of a new class of normalized multivalent harmonic functions in the open unit disk are analyzed, including bounds on coefficients, growth estimations, starlikeness and convexity radii. It is further demonstrated that this class is closed when its members [...] Read more.

In this paper, various features of a new class of normalized multivalent harmonic functions in the open unit disk are analyzed, including bounds on coefficients, growth estimations, starlikeness and convexity radii. It is further demonstrated that this class is closed when its members are convoluted. It can also be seen that various previously introduced and investigated classes of multivalent harmonic functions appear as special cases for this class. Full article

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

9 pages, 269 KiB

Open AccessArticle

Application of the Quasi-Hadamard Product to Subclasses of Analytic Functions Involving the q-Difference Operator

by Wafaa Y. Kota, Rabha M. El-Ashwah and Nicoleta Breaz

Mathematics 2023, 11(10), 2291; https://doi.org/10.3390/math11102291 - 15 May 2023

Viewed by 1056

Abstract

In this study, the subclasses

V_{q, ϱ}^{ℓ} (c_{𝚥}, λ),

U_{q, ϱ} (c_{𝚥}, λ)

and

V_{q, ϱ} (c_{𝚥}, λ)

of analytic functions using the [...] Read more.

In this study, the subclasses

V_{q, ϱ}^{ℓ} (c_{𝚥}, λ),

U_{q, ϱ} (c_{𝚥}, λ)

and

V_{q, ϱ} (c_{𝚥}, λ)

of analytic functions using the q-difference operator are defined and investigated. Thus, we obtained some results for the quasi-Hadamard product on these classes of analytic functions. Furthermore, connections between our results and some previously established results are outlined in this study. Full article

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

11 pages, 295 KiB

Open AccessArticle

Studying the Harmonic Functions Associated with Quantum Calculus

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

Mathematics 2023, 11(10), 2220; https://doi.org/10.3390/math11102220 - 9 May 2023

Cited by 9 | Viewed by 1676

Abstract

Using the derivative operators’

q

-analogs values, a wide variety of holomorphic function subclasses,

q

-starlike, and

q

-convex functions have been researched and examined. With the aid of fundamental ideas from the theory of

q

-calculus operators, we describe new

q

-operators [...] Read more.

Using the derivative operators’

q

-analogs values, a wide variety of holomorphic function subclasses,

q

-starlike, and

q

-convex functions have been researched and examined. With the aid of fundamental ideas from the theory of

q

-calculus operators, we describe new

q

-operators of harmonic function

H_{ϱ, χ; q}^{γ} F (ϖ)

in this work. We also define a new harmonic function subclass related to the Janowski and

q

-analog of Le Roy-type functions Mittag–Leffler functions. Several important properties are assigned to the new class, including necessary and sufficient conditions, the covering Theorem, extreme points, distortion bounds, convolution, and convex combinations. Furthermore, we emphasize several established remarks for confirming our primary findings presented in this study, as well as some applications of this study in the form of specific outcomes and corollaries. Full article

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

20 pages, 334 KiB

Open AccessArticle

Sharp Coefficient Bounds for a New Subclass of Starlike Functions of Complex Order γ Associated with Cardioid Domain

by Suha B. Al-Shaikh, Khaled Matarneh, Ahmad A. Abubaker and Mohammad Faisal Khan

Mathematics 2023, 11(9), 2017; https://doi.org/10.3390/math11092017 - 24 Apr 2023

Viewed by 1107

Abstract

In this study, by using the concepts of subordination, we define a new family

R (M, N, λ, γ)

of starlike functions of complex order

γ

connected with the cardioid domain. The main contribution of this article consists of the [...] Read more.

In this study, by using the concepts of subordination, we define a new family

R (M, N, λ, γ)

of starlike functions of complex order

γ

connected with the cardioid domain. The main contribution of this article consists of the derivations of sharp inequality, considering the functions belonging to the family

R (M, N, λ, γ)

of starlike functions in

U

. Particularly, sharp bounds of the first two Taylor–Maclaurin coefficients, sharp estimates of the Fekete–Szegö-type functionals, and coefficient inequalities are investigated for this newly defined family

R (M, N, λ, γ)

of starlike functions. Furthermore, for the inverse function and the

log (\frac{g (z)}{z})

function, we investigate the same types of problems. Several well-known corollaries are also highlighted to show the connections between prior research and the new findings. Full article

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

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