scholarly journals Quasiconformality of harmonic mappings between Jordan domains

Filomat ◽  
2010 ◽  
Vol 24 (3) ◽  
pp. 111-125 ◽  
Author(s):  
Miodrag Mateljevic ◽  
Vladimir Bozin ◽  
Miljan Knezevic
Keyword(s):  
Unit Disc ◽  
Necessary Conditions ◽  
Harmonic Mapping ◽  
Boundary Function ◽  
Harmonic Mappings ◽  
Existence Problem ◽  
Sufficient And Necessary Conditions

Suppose that h is a harmonic mapping of the unit disc onto a C 1,? domain D. We give sufficient and necessary conditions in terms of boundary function that h is q.c. We announce some new results and also outline application to existence problem of mean distortion minimizers in the Universal Teichm?ller space.

scholarly journals Quasiconformality of harmonic mappings between Jordan domains

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 479-510 ◽  
Author(s):  
Miodrag Mateljevic
Keyword(s):  
Half Plane ◽  
Unit Disc ◽  
Necessary Conditions ◽  
Harmonic Mapping ◽  
Boundary Function ◽  
Harmonic Mappings ◽  
C1 Domain ◽  
Sufficient And Necessary Conditions ◽  
Upper Half Plane

Suppose that h is a harmonic mapping of the unit disc onto a C1, ? domain D. Then h is q.c. if and only if it is bi-Lipschitz. In particular, we consider sufficient and necessary conditions in terms of boundary function that h is q.c. We give a review of recent related results including the case when domain is the upper half plane. We also consider harmonic mapping with respect to ? metric on codomain.

scholarly journals The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
Maisarah Haji Mohd ◽  
Maslina Darus
Keyword(s):  
Unit Disc ◽  
Harmonic Mapping ◽  
Starlike Functions ◽  
Starlike Function ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form defined on the open unit disc . The functions are in the class of the generalized Janowski starlike log-harmonic mapping, , with the functional in the class of the generalized Janowski starlike functions, . By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, .

Neighborhoods for certain analytic functions

2016 ◽  
Vol 09 (04) ◽  
pp. 1650083
Author(s):  
Y. Talafha ◽  
B. A. Frasin ◽  
Tariq Al-Hawary ◽  
R. Bani Ata
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Necessary Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Jack’S Lemma ◽  
Sufficient And Necessary Conditions ◽  
Jack's Lemma

In this paper, we introduce the neighborhood [Formula: see text] of analytic functions [Formula: see text] and [Formula: see text] defined in the open unit disc. Furthermore, we derive some sufficient and necessary conditions to be in [Formula: see text]. In addition, we see some applications of Jack’s lemma.

scholarly journals REMARKS ON THE UNIVALENCE CRITERION OF PASCU AND PASCU

2013 ◽  
Vol 89 (2) ◽  
pp. 210-216
Author(s):  
VAIDHYANATHAN BHARANEDHAR ◽  
SAMINATHAN PONNUSAMY
Keyword(s):  
Recent Work ◽  
Unit Disc ◽  
Univalent Functions ◽  
Harmonic Mapping ◽  
Harmonic Mappings ◽  
Univalence Criterion ◽  
Coefficient Condition

AbstractWe consider a recent work of Pascu and Pascu [‘Neighbourhoods of univalent functions’,Bull. Aust. Math. Soc. 83(2) (2011), 210–219] and rectify an error that appears in their work. In addition, we study certain analogous results for sense-preserving harmonic mappings in the unit disc$\vert z\vert \lt 1$. As a corollary to this result, we derive a coefficient condition for a sense-preserving harmonic mapping to be univalent in$\vert z\vert \lt 1$.

scholarly journals Oscillation of Second-Order Differential Equations with Multiple and Mixed Delays under a Canonical Operator

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1323
Author(s):  
Shyam Sundar Santra ◽  
Rami Ahmad El-Nabulsi ◽  
Khaled Mohamed Khedher
Keyword(s):  
Differential Equations ◽  
Necessary Conditions ◽  
Second Order ◽  
Multiple Delays ◽  
Mixed Delays ◽  
Neutral Differential Equations ◽  
Canonical Operator ◽  
Second Order Differential Equations ◽  
The Future ◽  
Sufficient And Necessary Conditions

In this work, we obtained new sufficient and necessary conditions for the oscillation of second-order differential equations with mixed and multiple delays under a canonical operator. Our methods could be applicable to find the sufficient and necessary conditions for any neutral differential equations. Furthermore, we proved the validity of the obtained results via particular examples. At the end of the paper, we provide the future scope of this study.

scholarly journals Properties of Certain Subclass of Meromorphic Multivalent Functions Associated with q-Difference Operator

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1035
Author(s):  
Cai-Mei Yan ◽  
Rekha Srivastava ◽  
Jin-Lin Liu
Keyword(s):  
Difference Operator ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Radius Of Starlikeness ◽  
Closure Theorems ◽  
Sufficient And Necessary Conditions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

A new subclass Σp,q(α,A,B) of meromorphic multivalent functions is defined by means of a q-difference operator. Some properties of the functions in this new subclass, such as sufficient and necessary conditions, coefficient estimates, growth and distortion theorems, radius of starlikeness and convexity, partial sums and closure theorems, are investigated.

Perfect colorings of patterns with multiple orbits

2019 ◽  
Vol 75 (6) ◽  
pp. 814-826
Author(s):  
Allan Junio ◽  
Ma. Lailani Walo
Keyword(s):  
Necessary Conditions ◽  
Sufficient And Necessary Conditions

This paper studies colorings of patterns with multiple orbits, particularly those colorings where the orbits share colors. The main problem is determining when such colorings become perfect. This problem is attacked by characterizing all perfect colorings of patterns through the construction of sufficient and necessary conditions for a coloring to be perfect. These results are then applied on symmetrical objects to construct both perfect and non-perfect colorings.

scholarly journals On a Periodic Predator-Prey System with Holling III Functional Response and Stage Structure for Prey

2010 ◽  
Vol 2010 ◽  
pp. 1-12
Author(s):  
Xiangzeng Kong ◽  
Zhiqin Chen ◽  
Li Xu ◽  
Wensheng Yang
Keyword(s):  
Functional Response ◽  
Prey Species ◽  
Necessary Conditions ◽  
Stage Structure ◽  
Predator Prey ◽  
Prey System ◽  
Sufficient And Necessary Conditions ◽  
Holling Iii Functional Response

We propose and study the permanence of the following periodic Holling III predator-prey system with stage structure for prey and both two predators which consume immature prey. Sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained.

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