scholarly journals New Subclasses of Multivalent Analytic Functions Associated with a Linear Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Ding-Gong Yang ◽  
Jin-Lin Liu
Keyword(s):  
Linear Operator ◽  
Analytic Functions

Differential sandwich theorems of p-valent functions defined by a certain linear operator

2016 ◽  
Vol 53 (2) ◽  
pp. 131-137
Author(s):  
Ping He ◽  
Defei Zhang
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Differential Subordination ◽  
Sandwich Type ◽  
Differential Subordination And Superordination

In this paper we introduce differential subordination and superordination properties for certain subclasses of analytic functions involving certain linear operator, and obtain sandwich-type results for the functions belonging to these classes.

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 Subordination and superordination results of p-valent analytic functions involving a linear operator

2017 ◽  
Vol 35 (2) ◽  
pp. 223 ◽  
Author(s):  
Tamer M. Seoudy
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

In this paper we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by a class of a linear operator. Some of our results improve and generalize previously known results.

scholarly journals Expansion of analytic functions of an operator in series of Faber polynomials

1997 ◽  
Vol 56 (2) ◽  
pp. 303-318 ◽  
Author(s):  
Maurice Hasson
Keyword(s):  
Banach Space ◽  
Linear Operator ◽  
Analytic Functions ◽  
Bounded Linear Operator ◽  
Complex Banach Space ◽  
Faber Polynomials ◽  
Bounded Linear ◽  
In Series ◽  
Image Position

Let T: B → B be a bounded linear operator on the complex Banach space B and let f(z) be analytic on a domain D containing the spectrum Sp(T) of T. Then f(T) is defined bywhere C is a contour surrounding SP(T) and contained in D.

scholarly journals Connections between Certain Subclasses of Analytic Univalent Functions Based on Operators

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
R. Ezhilarasi ◽  
T. V. Sudharsan ◽  
Maisarah Haji Mohd ◽  
K. G. Subramanian
Keyword(s):  
Linear Operator ◽  
Integral Operator ◽  
Hypergeometric Function ◽  
Analytic Functions ◽  
Univalent Functions

In this paper, by applying the Hohlov linear operator, connections between the class SD(α),  α≥0, and two subclasses of the class A of normalized analytic functions are established. Also an integral operator related to hypergeometric function is considered.

scholarly journals Mapping properties for convolutions involving hypergeometric functions

2003 ◽  
Vol 2003 (17) ◽  
pp. 1083-1091 ◽  
Author(s):  
J. A Kim ◽  
K. H. Shon
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disk

Forμ≥0, we consider a linear operatorLμ:A→Adefined by the convolutionfμ∗f, wherefμ=(1−μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z))′. Letφ∗(A,B)denote the class of normalized functionsfwhich are analytic in the open unit disk and satisfy the conditionzf′/f≺(1+Az)/1+Bz,−1≤A<B≤1, and letRη(β)denote the class of normalized analytic functionsffor which there exits a numberη∈(−π/2,π/2)such thatRe(eiη(f′(z)−β))>0,(β<1). The main object of this paper is to establish the connection betweenRη(β)andφ∗(A,B)involving the operatorLμ(f). Furthermore, we treat the convolutionI=∫0z(fμ(t)/t)dt ∗f(z)forf∈Rη(β).

New subclass of analytic functions in conical domain associated with a linear operator

2016 ◽  
Vol 36 (3) ◽  
pp. 704-716 ◽  
Author(s):  
Muhammed ARIF ◽  
Shahid MAHMOOD ◽  
Janusz SOKÓŁ ◽  
Jacek DZIOK
Keyword(s):  
Linear Operator ◽  
Analytic Functions
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