scholarly journals Sufficient conditions for strongly Carathéodory functions

2011 ◽  
Vol 62 (8) ◽  
pp. 2978-2987 ◽  
Author(s):  
Hitoshi Shiraishi ◽  
Shigeyoshi Owa ◽  
H.M. Srivastava
Keyword(s):  
Sufficient Conditions ◽  
Carathéodory Functions

scholarly journals Sufficient conditions for Carathéodory functions

2006 ◽  
Vol 51 (3-4) ◽  
pp. 467-474 ◽  
Author(s):  
Dingong Yang ◽  
Shigeyoshi Owa
Keyword(s):  
Sufficient Conditions ◽  
Carathéodory Functions

Some applications of first-order differential subordinations

2017 ◽  
Vol 67 (4) ◽  
Author(s):  
Mamoru Nunokawa ◽  
Janusz Sokół
Keyword(s):  
Sufficient Conditions ◽  
Geometric Approach ◽  
Differential Subordination ◽  
First Order ◽  
Carathéodory Functions ◽  
Subordination Theory ◽  
Differential Subordinations

AbstractIn this work we present a new geometric approach to some problems in differential subordination theory. In the paper some sufficient conditions for function to be starlike or univalent or to be in the class of Carathéodory functions are obtained. We also discuss the new results closely related to the generalized Briot-Bouquet differential subordination.

scholarly journals On the existence of positive solutions for periodic parabolic sublinear problems

2003 ◽  
Vol 2003 (17) ◽  
pp. 975-984 ◽  
Author(s):  
T. Godoy ◽  
U. Kaufmann
Keyword(s):  
Bounded Domain ◽  
Positive Solutions ◽  
Wide Class ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Parabolic Problems ◽  
Smooth Bounded Domain ◽  
Carathéodory Functions ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

We give necessary and sufficient conditions for the existence of positive solutions for sublinear Dirichlet periodic parabolic problemsLu=g(x,t,u)inΩ×ℝ(whereΩ⊂ℝNis a smooth bounded domain) for a wide class of Carathéodory functionsg:Ω×ℝ×[0,∞)→ℝsatisfying some integrability and positivity conditions.

scholarly journals Sufficient conditions for a certain general class of Carathéodory functions

Filomat ◽  
2016 ◽  
Vol 30 (13) ◽  
pp. 3615-3625 ◽  
Author(s):  
Qing-Hua Xu ◽  
Ting Yang ◽  
H.M. Srivastava
Keyword(s):  
Unit Disk ◽  
General Class ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Carathéodory Functions

In the present paper, the authors derive sufficient conditions for functions to be in a certain general class of Carath?odory functions in the open unit disk by using the Miller-Mocanu lemma. As an application of our main result, we deduce sufficient conditions for functions belonging to the class ST ?u? which is introduced here. The various results presented here would generalize and extend many known results.

Sufficient conditions for Carathéodory functions and applications to univalent functions

2019 ◽  
Vol 69 (5) ◽  
pp. 1065-1076
Author(s):  
Oh Sang Kwon ◽  
Young Jae Sim
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Univalent Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Geometric Properties ◽  
First Order ◽  
Carathéodory Functions ◽  
Carathéodory Function

Abstract In this paper, the authors derive several sufficient conditions for a function to be the Carathéodory function in the unit disk 𝔻: = {z ∈ ℂ: |z| < 1}. More precisely, for given β ∈ (–π/2, π/2), γ ∈ [0, cosβ) and δ ∈ (0, π/2], we find some sufficient conditions for an analytic function p such that p(0) = 1 to satisfy Re{e−iβ p(z)} > γ or | arg {p(z)–γ} | < δ for all z ∈ 𝔻 by using the first-order differential subordination. We then apply the results obtained here in order to find some conditions for univalent functions with geometric properties such as spirallikeness and strongly starlikeness.

scholarly journals Sufficient conditions for Carathéodory functions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 1097-1106 ◽  
Author(s):  
Mamoru Nunokawa ◽  
Oh Kwon ◽  
Young Sim ◽  
Nak Cho
Keyword(s):  
Unit Disk ◽  
Sufficient Conditions ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Carathéodory Functions ◽  
Special Cases

In the present paper, we obtain several sufficient conditions for Carath?odory functions in the open unit disk U = {z ? C : ?z? < 1}. We also obtain sufficient conditions for p-valent or starlike functions. Moreover, we improve some results due to Nunokawa [Tsukuba J. Math. 13 (1989), 453-455] as some special cases of main results.

scholarly journals On application of differential subordination for Carathéodory functions

2020 ◽  
Vol 12 (2) ◽  
pp. 370-382
Author(s):  
V. Agnes Sagaya Judy Lavanya ◽  
M. P. Jeyaraman ◽  
H. Aaisha Farzana
Keyword(s):  
Analytic Functions ◽  
Sufficient Conditions ◽  
Differential Subordination ◽  
Carathéodory Functions ◽  
Special Cases

AbstractNew sufficient conditions involving the properties of analytic functions to belong to the class of Carathéodory functions are investigated. Certain univalence and starlikeness conditions are deduced as special cases of main results.

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