scholarly journals Coefficient inequalities for certain classes of analytic function using q−derivatives

Mathematica ◽  
2020 ◽  
Vol 62 (85) (2) ◽  
pp. 189-197
Author(s):  
S. Varadharajan ◽  
C. Selvaraj ◽  
K. R. Karthikeyan
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Operator Coefficient ◽  
Derivative Operator ◽  
Coefficient Inequalities

We introduce and we study certain classes of analytic functions which are defined by making use of the q-derivative operator. Coefficient inequalities for functions in these classes are discussed. Some interesting consequences of the results are also pointed out.

scholarly journals Second Hankel determinant for a class of analytic functions defined by q-derivative operator

2019 ◽  
Vol 27 (2) ◽  
pp. 167-177
Author(s):  
Dorina Răducanu
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Derivative Operator ◽  
Second Hankel Determinant

AbstractIn this paper, we obtain the estimates for the second Hankel determinant for a class of analytic functions defined by q-derivative operator and subordinate to an analytic function.

Results of differential subordination for a unified subclass of analytic functions defined using generalized Ruscheweyh derivative operator

2019 ◽  
Vol 12 (03) ◽  
pp. 1950035
Author(s):  
Ritu Agarwal ◽  
G. S. Paliwal ◽  
Parany Goswami
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Derivative Operator ◽  
Sandwich Theorem ◽  
Ruscheweyh Derivative Operator ◽  
Ruscheweyh Derivative ◽  
Principle Of Subordination ◽  
Coefficient Inequalities ◽  
Distortion Theorems

In this paper, we introduce a unified subclass of analytic functions by making use of the principle of subordination, involving generalized Ruscheweyh Derivative operator [Formula: see text]. The properties such as inclusion relationships, distortion theorems, coefficient inequalities and differential sandwich theorem for the above class have been discussed.

scholarly journals Kth Root Transformation for a subclass of Log-Sigmoid Analytic Function based on Quasi-Subordination

2018 ◽  
Vol 7 (4.10) ◽  
pp. 1007
Author(s):  
M. Hari Priya ◽  
R. Bharavi Sharma ◽  
V. Suman Kumar
Keyword(s):  
Analytic Function ◽  
Analytic Functions ◽  
Upper Bounds ◽  
Root Transformation ◽  
Coefficient Inequalities

In the present investigation, using the concept of quasi-subordination, two subclasses of analytic functions have been introduced. The coefficient inequalities, the Fekete-Szego inequality, upper bounds for kth  root transformation were studied. This study is extended to function  and for  . 

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 306 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Systematic Study ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Coefficient Inequalities

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

scholarly journals On Subclass of Analytic Univalent Functions Associated with Negative Coefficients

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Closure Theorems ◽  
Coefficient Inequalities ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems

M. H. Al-Abbadi and M. Darus (2009) recently introduced a new generalized derivative operatorμλ1,λ2n,m, which generalized many well-known operators studied earlier by many different authors. In this present paper, we shall investigate a new subclass of analytic functions in the open unit diskU={z∈ℂ:|z|<1}which is defined by new generalized derivative operator. Some results on coefficient inequalities, growth and distortion theorems, closure theorems, and extreme points of analytic functions belonging to the subclass are obtained.

scholarly journals Some classes of analytic and multivalent functions associated with q-derivative operators

2014 ◽  
Vol 6 (1) ◽  
pp. 5-23 ◽  
Author(s):  
S. D. Purohit ◽  
R. K. Raina
Keyword(s):  
Analytic Functions ◽  
Derivative Operator ◽  
Complex Order ◽  
Coefficient Inequalities

AbstractBy applying the q-derivative operator of order m (m ∈ ℕ0), we introduce two new subclasses of p-valently analytic functions of complex order. For these classes of functions, we obtain the coefficient inequalities and distortion properties. Some consequences of the main results are also considered

scholarly journals Partial sums and inclusion relations for analytic functions involving (p, q)-differential operator

2021 ◽  
Vol 19 (1) ◽  
pp. 329-337
Author(s):  
Huo Tang ◽  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Analytic Function ◽  
Differential Operator ◽  
Lower Bounds ◽  
Analytic Functions ◽  
Function Class ◽  
Partial Sums ◽  
Generalized Function ◽  
Inclusion Relations ◽  
Alpha Beta

Abstract Let f k ( z ) = z + ∑ n = 2 k a n z n {f}_{k}\left(z)=z+{\sum }_{n=2}^{k}{a}_{n}{z}^{n} be the sequence of partial sums of the analytic function f ( z ) = z + ∑ n = 2 ∞ a n z n f\left(z)=z+{\sum }_{n=2}^{\infty }{a}_{n}{z}^{n} . In this paper, we determine sharp lower bounds for Re { f ( z ) / f k ( z ) } {\rm{Re}}\{f\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}\left(z)\} , Re { f k ( z ) / f ( z ) } {\rm{Re}}\{{f}_{k}\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}f\left(z)\} , Re { f ′ ( z ) / f k ′ ( z ) } {\rm{Re}}\{{f}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}_{k}^{^{\prime} }\left(z)\} and Re { f k ′ ( z ) / f ′ ( z ) } {\rm{Re}}\{{f}_{k}^{^{\prime} }\left(z)\hspace{-0.08em}\text{/}\hspace{-0.08em}{f}^{^{\prime} }\left(z)\} , where f ( z ) f\left(z) belongs to the subclass J p , q m ( μ , α , β ) {{\mathcal{J}}}_{p,q}^{m}\left(\mu ,\alpha ,\beta ) of analytic functions, defined by Sălăgean ( p , q ) \left(p,q) -differential operator. In addition, the inclusion relations involving N δ ( e ) {N}_{\delta }\left(e) of this generalized function class are considered.

scholarly journals Coefficient inequalities for a class of analytic functions associated with the lemniscate of Bernoulli

2018 ◽  
Vol 37 (4) ◽  
pp. 83-95
Author(s):  
Trailokya Panigrahi ◽  
Janusz Sokól
Keyword(s):  
Upper Bound ◽  
Analytic Functions ◽  
Hankel Determinant ◽  
Lemniscate Of Bernoulli ◽  
Toeplitz Determinant ◽  
Second Hankel Determinant ◽  
Coefficient Inequalities ◽  
The Right

In this paper, a new subclass of analytic functions ML_{\lambda}^{*}  associated with the right half of the lemniscate of Bernoulli is introduced. The sharp upper bound for the Fekete-Szego functional |a_{3}-\mu a_{2}^{2}|  for both real and complex \mu are considered. Further, the sharp upper bound to the second Hankel determinant |H_{2}(1)| for the function f in the class ML_{\lambda}^{*} using Toeplitz determinant is studied. Relevances of the main results are also briefly indicated.

scholarly journals On Certain Subclasses of Analytic Functions Defined by Differential Subordination

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Hesam Mahzoon
Keyword(s):  
Analytic Functions ◽  
Differential Subordination ◽  
Radius Of Starlikeness ◽  
Covering Theorems ◽  
Coefficient Inequalities

We introduce and study certain subclasses of analytic functions which are defined by differential subordination. Coefficient inequalities, some properties of neighborhoods, distortion and covering theorems, radius of starlikeness, and convexity for these subclasses are given.

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