Generalization of the $${\varvec{lq}}$$lq-modular closure theorem and applications

2018 ◽  
Vol 112 (4) ◽  
pp. 361-370
Author(s):  
El Hassane Fliouet
Keyword(s):  
Closure Theorem

Closure Theorem for Analytic Subgroups of Real Lie Groups

1976 ◽  
Vol 19 (4) ◽  
pp. 435-439 ◽  
Author(s):  
D. Ž. Djoković
Keyword(s):  
Lie Groups ◽  
Lie Group ◽  
Closed Subgroup ◽  
Main Result Theorem ◽  
Closure Theorem ◽  
Result Theorem ◽  
Analytic Subgroup

Let G be a real Lie group, A a closed subgroup of G and B an analytic subgroup of G. Assume that B normalizes A and that AB is closed in G. Then our main result (Theorem 1) asserts that .This result generalizes Lemma 2 in the paper [4], G. Hochschild has pointed out to me that the proof of that lemma given in [4] is not complete but that it can be easily completed.

scholarly journals Subclasses of Starlike Functions Associated with Fractional q-Calculus Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
C. Selvaraj ◽  
O. S. Babu
Keyword(s):  
Extreme Points ◽  
Starlike Functions ◽  
Partial Sums ◽  
Coefficient Estimate ◽  
Integral Means ◽  
Closure Theorem ◽  
Distortion Bounds

Making use of fractional q-calculus operators, we introduce a new subclass ℳq(λ,γ,k) of starlike functions and determine the coefficient estimate, extreme points, closure theorem, and distortion bounds for functions in ℳq(λ,γ,k). Furthermore we discuss neighborhood results, subordination theorem, partial sums, and integral means inequalities for functions in ℳq(λ,γ,k).

scholarly journals Some Geometric Properties for a Certain Class of Meromorphic Univalent Functions by Differential Operator

2021 ◽  
pp. 2667-2675
Author(s):  
Mohammed Hadi Lafta
Keyword(s):  
Differential Operator ◽  
Hadamard Product ◽  
Convex Combination ◽  
Univalent Functions ◽  
Integral Operators ◽  
Coefficient Estimates ◽  
Growth Theorem ◽  
Closure Theorem ◽  
Major Target ◽  
Meromorphic Univalent Functions

The major target of this paper is to study a confirmed class of meromorphic univalent functions . We procure several results, such as those related to coefficient estimates, distortion and growth theorem, radii of starlikeness, and convexity for this class, n additionto hadamard product, convex combination, closure theorem, integral operators, and  neighborhoods.

scholarly journals Weak Closure Theorem fails for Z2-actions

2002 ◽  
Vol 153 (2) ◽  
pp. 115-125 ◽  
Author(s):  
T. Downarowicz ◽  
J. Kwiatkowski
Keyword(s):  
Closure Theorem ◽  
Weak Closure

scholarly journals On q-analogue of Janowski-type starlike functions with respect to symmetric points

2021 ◽  
Vol 54 (1) ◽  
pp. 37-46
Author(s):  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Raees Khan ◽  
Muhammad Zubair ◽  
Zabidin Salleh
Keyword(s):  
Extreme Point ◽  
Point Theorem ◽  
Starlike Functions ◽  
Circular Domain ◽  
Distortion Theorem ◽  
Geometric Properties ◽  
Coefficient Bounds ◽  
Closure Theorem ◽  
Symmetric Points

Abstract The main objective of the present paper is to define a class of q q -starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.

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