scholarly journals Certain Class of Bi-Bazilevic Functions with Bounded Boundary Rotation Involving Salăgeăn Operator

2020 ◽  
Author(s):  
Mohamed Kamal AOUF ◽  
Tamer SEOUDY
Keyword(s):  
Sălăgean Operator ◽  
Salagean Operator ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Bazilevic Functions

scholarly journals Some properties for certain class of bi-univalent functions defined by $ q $-Cătaş operator with bounded boundary rotation

2021 ◽  
Vol 7 (1) ◽  
pp. 903-914
Author(s):  
S. M. Madian ◽  
Keyword(s):  
Univalent Functions ◽  
Additional Parameter ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Bazilevic Functions

<abstract><p>Throughout the paper, we introduce a new subclass $ \mathcal{H}_{\alpha, \mu, \rho, m, \beta }^{n, q, \lambda, l}\ f(z)$ by using the Bazilevič functions with the idea of bounded boundary rotation and $ q $-analogue Cătaş operator. Also we find the estimate of the coefficients for functions in this class. Finally, in the concluding section, we have chosen to reiterate the well-demonstrated fact that any attempt to produce the rather straightforward $ (p, q) $-variations of the results, which we have presented in this article, will be a rather trivial and inconsequential exercise, simply because the additional parameter $ p $ is obviously redundant.</p></abstract>

Toeplitz matrices whose elements are coefficients of Bazilevič functions

2018 ◽  
Vol 16 (1) ◽  
pp. 1161-1169
Author(s):  
Varadharajan Radhika ◽  
Jay M. Jahangiri ◽  
Srikandan Sivasubramanian ◽  
Gangadharan Murugusundaramoorthy
Keyword(s):  
Convex Functions ◽  
Toeplitz Matrices ◽  
Upper Bounds ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation ◽  
Bazilevic Functions ◽  
Class Of Functions

AbstractWe consider the Toeplitz matrices whose elements are the coefficients of Bazilevič functions and obtain upper bounds for the first four determinants of these Toeplitz matrices. The results presented here are new and noble and the only prior compatible results are the recent publications by Thomas and Halim [1] for the classes of starlike and close-to-convex functions and Radhika et al. [2] for the class of functions with bounded boundary rotation.

scholarly journals -Bazilevic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
F. M. Al-Oboudi
Keyword(s):  
Inclusion Relation ◽  
Coefficient Bounds ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Convolution Properties ◽  
Bazilevic Functions

The aim of this paper is to define and study a class of Bazilevic functions using the generalized Salagean operator. Some properties of this class are investigated: inclusion relation, some convolution properties, coefficient bounds, and other interesting results.

On the class of harmonic mappings which is related to the class of bounded boundary rotation

2015 ◽  
Vol 267 ◽  
pp. 790-794
Author(s):  
Yaşar Polatog̃lu ◽  
Melike Aydog̃an ◽  
Yasemin Kahramaner
Keyword(s):  
Harmonic Mappings ◽  
Bounded Boundary Rotation ◽  
Boundary Rotation
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