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20 pages, 372 KiB

Open AccessArticle

Subclasses of Noshiro-Type Starlike Harmonic Functions Involving q-Srivastava–Attiya Operator

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

Mathematics 2023, 11(23), 4711; https://doi.org/10.3390/math11234711 - 21 Nov 2023

Cited by 6 | Viewed by 1106

In this paper, the harmonic function related to the q-Srivastava–Attiya operator is described to introduce a new class of complex harmonic functions that are orientation-preserving and univalent in the open-unit disk. We also cover some important aspects such as coefficient bounds, convolution conservation, and convexity constraints. Next, using sufficiency criteria, we calculate the sharp bounds of the real parts of the ratios of harmonic functions to their sequences of partial sums. In addition, for the first time some of the interesting implications of the q-Srivastava–Attiya operator in harmonic functions are also included. Full article

17 pages, 351 KiB

Open AccessArticle

Sandwich-Type Theorems for a Family of Non-Bazilevič Functions Involving a q-Analog Integral Operator

by Sarem H. Hadi, Maslina Darus, Firas Ghanim and Alina Alb Lupaş

Mathematics 2023, 11(11), 2479; https://doi.org/10.3390/math11112479 - 28 May 2023

Cited by 7 | Viewed by 1410

Abstract

This article presents a new q-analog integral operator, which generalizes the q-Srivastava–Attiya operator. Using this q-analog operator, we define a family of analytic non-Bazilevič functions, denoted as [...] Read more.

T_{q, τ + 1, u}^{μ} (ϑ, λ, M, N)

. Furthermore, we investigate the differential subordination properties of univalent functions using q-calculus, which includes the best dominance, best subordination, and sandwich-type properties. Our results are proven using specialized techniques in differential subordination theory. Full article

(This article belongs to the Special Issue Fractional Calculus and Mathematical Applications)

10 pages, 284 KiB

Open AccessArticle

On Generalizations of the Close-to-Convex Functions Associated with

q

-Srivastava–Attiya Operator

by Daniel Breaz, Abdullah A. Alahmari, Luminiţa-Ioana Cotîrlă and Shujaat Ali Shah

Mathematics 2023, 11(9), 2022; https://doi.org/10.3390/math11092022 - 24 Apr 2023

Cited by 8 | Viewed by 1700

Abstract

The study of the

q

-analogue of the classical results of geometric function theory is currently of great interest to scholars. In this article, we define generalized classes of close-to-convex functions and quasi-convex functions with the help of the

q

-difference operator. Moreover, [...] Read more.

The study of the

q

q

-difference operator. Moreover, by using the

q

-analogues of a certain family of linear operators, the classes

K_{q, b}^{s} (h)

{\tilde{K}}_{q, s}^{b} (h)

Q_{q, b}^{s} (h)

, and

{\tilde{Q}}_{q, s}^{b} (h)

are introduced. Several interesting inclusion relationships between these newly defined classes are discussed, and the invariance of these classes under the

q

-Bernadi integral operator was examined. Furthermore, some special cases and useful consequences of these investigations were taken into consideration. Full article

(This article belongs to the Special Issue Complex Analysis and Geometric Function Theory)

12 pages, 308 KiB

Open AccessArticle

Certain Inclusion Properties for the Class of q-Analogue of Fuzzy α-Convex Functions

by Abdel Fatah Azzam, Shujaat Ali Shah, Alhanouf Alburaikan and Sheza M. El-Deeb

Symmetry 2023, 15(2), 509; https://doi.org/10.3390/sym15020509 - 14 Feb 2023

Cited by 6 | Viewed by 1658

Abstract

Recently, the properties of analytic functions have been mainly discussed by means of a fuzzy subset and a q-difference operator. We define certain new subclasses of analytic functions by using the fuzzy subordination to univalent functions whose range is symmetric with respect to the real axis. We introduce the family of linear q-operators and define various classes associated with these operators. The inclusion results and various integral properties are the main investigations of this article. Full article

(This article belongs to the Special Issue Symmetry in Functional Equations and Analytic Inequalities III)

9 pages, 287 KiB

Open AccessArticle

New Applications of Gegenbauer Polynomials on a New Family of Bi-Bazilevič Functions Governed by the q-Srivastava-Attiya Operator

by Abbas Kareem Wanas and Luminiţa-Ioana Cotîrlǎ

Mathematics 2022, 10(8), 1309; https://doi.org/10.3390/math10081309 - 14 Apr 2022

Cited by 11 | Viewed by 2098

Abstract

In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family

J_{Σ} (λ, γ, s, t, q; h)

of holomorphic and bi-univalent functions which were defined in the unit disk [...] Read more.

In the present paper, making use of Gegenbauer polynomials, we initiate and explore a new family

J_{Σ} (λ, γ, s, t, q; h)

of holomorphic and bi-univalent functions which were defined in the unit disk

D

associated with the q-Srivastava–Attiya operator. We establish the bounds for

| a_{2} |

and

| a_{3} |

, where

a_{2}

a_{3}

are the initial Taylor–Maclaurin coefficients. For the new family of functions

J_{Σ} (λ, γ, s, t, q; h)

we investigate the Fekete-Szegö inequality, special cases and consequences. Full article

(This article belongs to the Special Issue New Trends in Complex Analysis Researches)

14 pages, 329 KiB

Open AccessArticle

Applications of the q-Srivastava-Attiya Operator Involving a Certain Family of Bi-Univalent Functions Associated with the Horadam Polynomials

by Hari Mohan Srivastava, Abbas Kareem Wanas and Rekha Srivastava

Symmetry 2021, 13(7), 1230; https://doi.org/10.3390/sym13071230 - 8 Jul 2021

Cited by 62 | Viewed by 3928

Abstract

In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family

{SW}_{Σ} (δ, γ, λ, s, t, q, r)

of normalized holomorphic and bi-univalent functions in the [...] Read more.

In this article, by making use of the q-Srivastava-Attiya operator, we introduce and investigate a new family

{SW}_{Σ} (δ, γ, λ, s, t, q, r)

of normalized holomorphic and bi-univalent functions in the open unit disk

U

, which are associated with the Bazilevič functions and the

λ

-pseudo-starlike functions as well as the Horadam polynomials. We estimate the second and the third coefficients in the Taylor-Maclaurin expansions of functions belonging to the holomorphic and bi-univalent function class, which we introduce here. Furthermore, we establish the Fekete-Szegö inequality for functions in the family

{SW}_{Σ} (δ, γ, λ, s, t, q, r)

. Relevant connections of some of the special cases of the main results with those in several earlier works are also pointed out. Our usage here of the basic or quantum (or q-) extension of the familiar Hurwitz-Lerch zeta function

Φ (z, s, a)

is justified by the fact that several members of this family of zeta functions possess properties with local or non-local symmetries. Our study of the applications of such quantum (or q-) extensions in this paper is also motivated by the symmetric nature of quantum calculus itself. Full article

(This article belongs to the Special Issue Functional Equations and Analytic Inequalities)

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