Linear Operator on univalent Function of Complex Order

2010 ◽  
Author(s):  
Essam Aqlan
Keyword(s):  
Linear Operator ◽  
Univalent Function ◽  
Complex Order

Majorization of starlike and convex functions of complex order involving linear operators

2016 ◽  
Vol 66 (1) ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
K. Thilagavathi
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Analytic Functions ◽  
Linear Operators ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractThe main object of this present paper is to investigate the problem of majorization of certain class of analytic functions of complex order defined by the Dziok-Raina linear operator. Moreover we point out some new or known consequences of our main result.

scholarly journals Convolution properties for subclasses of meromorphic univalent functions of complex order

Filomat ◽  
2012 ◽  
Vol 26 (1) ◽  
pp. 153-163 ◽  
Author(s):  
Teodor Bulboacă ◽  
Mohamed Aouf ◽  
Rabha El-Ashwah
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Complex Order ◽  
Inclusion Relations ◽  
Coefficient Inequalities ◽  
Convolution Properties ◽  
Meromorphic Univalent Functions

Using the new linear operator Lm(?,l)f(z) = 1/z + ??k=1(l/l+ ?k)m akzk-1, f ? ?, where l > 0, ? ? 0, and m ? N0 = N ? {0}, we introduce two subclasses of meromorphic analytic functions, and we investigate several convolution properties, coefficient inequalities, and inclusion relations for these classes.

scholarly journals Coefficient Estimates for Some Subclasses of m-Fold Symmetric Bi-univalent Functions Defined by Linear Operator

2021 ◽  
Vol 20 ◽  
pp. 115-120
Author(s):  
Dhirgam Allawy Hussein Hussein ◽  
Sahar Jaafar Mahmood
Keyword(s):  
Linear Operator ◽  
General Formula ◽  
Univalent Function ◽  
Symmetric Function ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Analytical Functions

 The articles introduces and investigates "two new subclasses of the bi-univalent functions ." These are analytical functions related to the m-fold symmetric function  and  .   We calculate the initial coefficients for all the functions that belong to them, as well as the coefficients for the functions that belong to a field where finding these coefficients requires a complicated method. Between the remaining results, the upper bounds for "the initial coefficients  "are found in our study as well as several examples. We also provide a general formula for the function and its inverse in the m-field. A function is called analytical if it does not take the same values twice .  It is called a univalent function if it is analytical at all its points, and the function is called a bi-univalent if it and its inverse are univalent functions together. We also discuss other concepts and important terms.   .

scholarly journals Certain Classes of Univalent Functions With Negative Coefficients Defined By General Linear Operator

2019 ◽  
Vol 24 (7) ◽  
pp. 129
Author(s):  
Mazin Sh.Mahmoud1 ◽  
Abdul Rahman S.Juma ◽  
, Raheam A. Mansor Al-Saphory3
Keyword(s):  
Linear Operator ◽  
Hypergeometric Function ◽  
Univalent Function ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
Univalent Functions ◽  
General Linear ◽  
Class Of Functions

In this study, a subclass of an univalent function with negative coefficients which is defined by anew general Linear operator have been introduced. The sharp results for coefficients estimators, distortion and closure bounds, Hadamard product, and Neighborhood, and this paper deals with the utilizing of many of the results for classical hypergeometric function, where there can be generalized to m-hypergeometric functions. A subclasses of univalent functions are presented, and it has involving operator which generalizes many well-known. Denote A the class of functions f and  we have other results have been studied   http://dx.doi.org/10.25130/tjps.24.2019.140

On a Generalization of Bounded Univalent Function of Complex Order

2018 ◽  
Vol 15 (2) ◽  
pp. 601-605
Author(s):  
C. Ramachandran ◽  
T. Soupramanien ◽  
J. Sokół
Keyword(s):  
Differential Operator ◽  
Univalent Function ◽  
Analytic Functions ◽  
Differential Operators ◽  
Sufficient Conditions ◽  
Coefficient Estimates ◽  
New Class ◽  
Complex Order ◽  
Generalized Differential

In this paper, we introduce a new class of analytic functions of complex order involving a family of generalized differential operators and we discuss the sufficient conditions, estimation of coefficients. The motivation of this paper is to generalize the Coefficient Estimates obtained by Attiya, and Aouf et al. by making use of the generalized differential operator Dnλ, μ.

scholarly journals q-Generalized Linear Operator on Bounded Functions of Complex Order

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1149
Author(s):  
Rizwan Salim Badar ◽  
Khalida Inayat Noor
Keyword(s):  
Linear Operator ◽  
Function Theory ◽  
Geometric Function Theory ◽  
Integral Inclusion ◽  
Complex Order ◽  
Geometric Function ◽  
Bounded Functions

This article presents a q-generalized linear operator in Geometric Function Theory (GFT) and investigates its application to classes of analytic bounded functions of complex order S q ( c ; M ) and C q ( c ; M ) where 0 < q < 1 , 0 ≠ c ∈ C , and M > 1 2 . Integral inclusion of the classes related to the q-Bernardi operator is also proven.

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