Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 

Saved Queries

Sign in to use this feature.

Search Filter Reset All

Years

Between: -

Subjects

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Subjects Reset
Select Subjects

Journals

remove_circle_outline
remove_circle_outline
Add Journals Reset
Select Journals

Article Types

remove_circle_outline
Add Article Types Reset
Select Article Types

Countries / Regions

remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
remove_circle_outline
Add Countries / Regions Reset
Select Countries / Regions
Update Search
share announcement

Search Results (6)

Search Parameters:
Keywords = Schwarz Lemma

Order results
Result details
Results per page
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
13 pages, 285 KiB  
Article
Majorization Problems for Subclasses of Meromorphic Functions Defined by the Generalized q-Sălăgean Operator
by Ekram E. Ali, Rabha M. El-Ashwah, Teodor Bulboacă and Abeer M. Albalahi
Mathematics 2025, 13(10), 1612; https://doi.org/10.3390/math13101612 - 14 May 2025
Viewed by 306
Abstract
Using the generalized q-Sălăgean operator, we introduce a new class of meromorphic functions in a punctured unit disk U∗ and investigate a majorization problem associated with this class. The principal tool employed in this analysis is the recently established q-Schwarz–Pick [...] Read more.
Using the generalized q-Sălăgean operator, we introduce a new class of meromorphic functions in a punctured unit disk U∗ and investigate a majorization problem associated with this class. The principal tool employed in this analysis is the recently established q-Schwarz–Pick lemma. We investigate a majorization problem for meromorphic functions when the functions of the right hand side of the majorization belongs to this class. The main tool for this investigation is the generalization of Nehari’s lemma for the Jackson’s q-difference operator ∂q given recently by Adegani et al. Full article
(This article belongs to the Special Issue Advanced Research in Complex Analysis Operators and Special Classes of Analytic Functions)
11 pages, 282 KiB  
Article
Majorization Problem for q-General Family of Functions with Bounded Radius Rotations
by Kanwal Jabeen, Afis Saliu, Jianhua Gong and Saqib Hussain
Mathematics 2024, 12(17), 2605; https://doi.org/10.3390/math12172605 - 23 Aug 2024
Cited by 5 | Viewed by 930
Abstract
In this paper, we first prove the q-version of Schwarz Pick’s lemma. This result improved the one presented earlier in the literature without proof. Using this novel result, we study the majorization problem for the q-general class of functions with bounded [...] Read more.
In this paper, we first prove the q-version of Schwarz Pick’s lemma. This result improved the one presented earlier in the literature without proof. Using this novel result, we study the majorization problem for the q-general class of functions with bounded radius rotations, which we introduce here. In addition, the coefficient bound for majorized functions related to this class is derived. Relaxing the majorized condition on this general family, we obtain the estimate of coefficient bounds associated with the class. Consequently, we present new results as corollaries and point out relevant connections between the main results obtained from the ones in the literature. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory)
16 pages, 323 KiB  
Article
New Subclass of Close-to-Convex Functions Defined by Quantum Difference Operator and Related to Generalized Janowski Function
by Suha B. Al-Shaikh, Mohammad Faisal Khan, Mustafa Kamal and Naeem Ahmad
Symmetry 2023, 15(11), 1974; https://doi.org/10.3390/sym15111974 - 25 Oct 2023
Cited by 2 | Viewed by 1329
Abstract
This work begins with a discussion of the quantum calculus operator theory and proceeds to develop and investigate a new family of close-to-convex functions in an open unit disk. Considering the quantum difference operator, we define and study a new subclass of close-to-convex [...] Read more.
This work begins with a discussion of the quantum calculus operator theory and proceeds to develop and investigate a new family of close-to-convex functions in an open unit disk. Considering the quantum difference operator, we define and study a new subclass of close-to-convex functions connected with generalized Janowski functions. We prove the necessary and sufficient conditions for functions that belong to newly defined classes, including the inclusion relations and estimations of the coefficients. The Fekete–Szegő problem for a more general class is also discussed. The results of this investigation expand upon those of the previous study. Full article
(This article belongs to the Special Issue Symmetry in Geometric Theory of Analytic Functions)
20 pages, 336 KiB  
Article
New Criteria for Starlikness and Convexity of a Certain Family of Integral Operators
by Hari M. Srivastava, Rogayeh Alavi, Saeid Shams, Rasoul Aghalary and Santosh B. Joshi
Mathematics 2023, 11(18), 3919; https://doi.org/10.3390/math11183919 - 14 Sep 2023
Cited by 2 | Viewed by 1120
Abstract
In this paper, we first modify one of the most famous theorems on the principle of differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using this modified form, we generalize and improve several results, which [...] Read more.
In this paper, we first modify one of the most famous theorems on the principle of differential subordination to hold true for normalized analytic functions with a fixed initial Taylor-Maclaurin coefficient. By using this modified form, we generalize and improve several results, which appeared recently in the literature on the geometric function theory of complex analysis. We also prove some simple conditions for starlikeness, convexity, and the strong starlikeness of several one-parameter families of integral operators, including (for example) a certain μ-convex integral operator and the familiar Bernardi integral operator. Full article
(This article belongs to the Special Issue Current Topics in Geometric Function Theory)
9 pages, 244 KiB  
Article
On the Boundary Dieudonné–Pick Lemma
by Olga Kudryavtseva and Aleksei Solodov
Mathematics 2021, 9(10), 1108; https://doi.org/10.3390/math9101108 - 13 May 2021
Cited by 4 | Viewed by 1898
Abstract
The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of [...] Read more.
The class of holomorphic self-maps of a disk with a boundary fixed point is studied. For this class of functions, the famous Julia–Carathéodory theorem gives a sharp estimate of the angular derivative at the boundary fixed point in terms of the image of the interior point. In the case when additional information about the value of the derivative at the interior point is known, a sharp estimate of the angular derivative at the boundary fixed point is obtained. As a consequence, the sharpness of the boundary Dieudonné–Pick lemma is established and the class of the extremal functions is identified. An unimprovable strengthening of the Osserman general boundary lemma is also obtained. Full article
7 pages, 207 KiB  
Article
A Refinement of Schwarz–Pick Lemma for Higher Derivatives
by Ern Gun Kwon, Jinkee Lee, Gun Kwon and Mi Hui Kim
Mathematics 2019, 7(1), 77; https://doi.org/10.3390/math7010077 - 13 Jan 2019
Cited by 1 | Viewed by 2549
Abstract
In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some [...] Read more.
In this paper, a Schwarz–Pick estimate of a holomorphic self map f of the unit disc D having the expansion f ( w ) = c 0 + c n ( w − z ) n + … in a neighborhood of some z in D is given. This result is a refinement of the Schwarz–Pick lemma, which improves a previous result of Shinji Yamashita. Full article
(This article belongs to the Section E1: Mathematics and Computer Science)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying article 1-50 on page 1 of 1.
Back to TopTop