Coefficient estimates in a class of functions from with prescribed third coefficientwith prescribed third coefficient

1984 ◽  
Vol 26 (6) ◽  
pp. 2360-2365 ◽  
Author(s):  
V. I. Kamotskii
Keyword(s):  
Coefficient Estimates ◽  
Class Of Functions

scholarly journals Coefficients estimates for functions inBn(α)

2003 ◽  
Vol 2003 (59) ◽  
pp. 3761-3767 ◽  
Author(s):  
S. Abdul Halim
Keyword(s):  
Differential Operator ◽  
Unit Disc ◽  
Coefficient Estimates ◽  
Class Of Functions

We consider functionsf, analytic in the unit disc and of the normalised formf(z)=z+∑k=2∞akzk. For functionsf∈Bn(α), the class of functions involving the Sălăgean differential operator, we give some coefficient estimates, namely,|a2|,|a3|, and|a4|.

scholarly journals ON A CLASS OF MEROMORPHIC STARLIKE FUNCTIONS WITH NEGATIVE COEFFICIENTS

1996 ◽  
Vol 27 (1) ◽  
pp. 15-26
Author(s):  
K. K. DIXIT ◽  
S. K. PAL
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Integral Transforms ◽  
Coefficient Estimates ◽  
Linear Combinations ◽  
Meromorphic Starlike Functions ◽  
Class Of Functions

Let $T^*_M(A, B, z_0)$ denote the class of functions \[f(z)=\frac{a}{z}-\sum_{n=1}^\infty a_nz^n, a\ge 1, a_n\ge 0\] regular and univalent in unit disc $U'=\{z:0<|z|<1\}$, satisfying the condition \[-z\frac{f'(z)}{f(z)}=\frac{1+Aw(z)}{1+Bw(z)}, \quad \text{ for } z\in U' \text{ and } w\in E\] (where $E$ is the class of analytic functions $w$ with $w(0) = 0$ and $|w(z)| \le 1$), where $-1\le A < B \le 1$, $0\le B \le 1$ and $f(z_0) =1/z_0$ ($0<z_0<1$). In this paper sharp coefficient estimates, distortion properties and radius of meromorphic convexity for functions in $T^*_M(A, B, z_0)$ have been obtained. We also study integral transforms of functions in $T^*_M(A, B, z_0)$. In the last, it is proved that the class $T^*_M(A, B, z_0)$ is closed under convex linear combinations.          

scholarly journals Coefficient estimates for starlike functions

1977 ◽  
Vol 16 (3) ◽  
pp. 415-425 ◽  
Author(s):  
M.L. Mogra ◽  
O.P. Juneja
Keyword(s):  
Unit Disc ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Michigan Math ◽  
Image Position ◽  
Class Of Functions

Let (α β) denote the class of functionsanalytic in the unit disc Δ ≡{z: |z| < 1} and satisfyingfor some α, β (0 ≤ α < 1, 0 < β ≤ 1) and for all z ∈ Δ. In the present paper, sharp coefficient estimates for functions in (α, β) have been obtained. The results thus obtained not only generalize the corresponding results of Thomas H. MacGregor (Michigan Math. J. 10 (1963), 277–281), A.V. Boyd (Proc. Amer. Math. Soc. 17 (1966), 1016–1018) and others, but also give rise to analogous results for various other subclasses of starlike functions.

scholarly journals Applications of Some Generalized Janowski Meromorphic Multivalent Functions

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Bakhtiar Ahmad ◽  
Muhammad Ghaffar Khan ◽  
Maslina Darus ◽  
Wali Khan Mashwani ◽  
Muhammad Arif
Keyword(s):  
Convex Combination ◽  
Coefficient Estimates ◽  
Geometric Properties ◽  
Growth Theorem ◽  
Quantum Calculus ◽  
Class Of Functions

In this article, the ideas of post-quantum calculus and meromorphic multivalent functions are combined and some applications of these functions are discussed. We introduce a new subclass of meromorphic multivalent functions in association with Janowski domain. We investigate and study some useful geometric properties of this class of functions such as sufficiency criteria, distortion problem, growth theorem, radii of starlikeness and convexity, convex combination, and coefficient estimates for this class.

scholarly journals COEFFICIENT ESTIMATES FOR BOUNDED STARLIKE FUNCTIONS OF COMPLEX ORDER

1994 ◽  
Vol 25 (2) ◽  
pp. 113-123
Author(s):  
M. K. AOUF
Keyword(s):  
Positive Integer ◽  
Starlike Functions ◽  
Coefficient Estimates ◽  
Complex Order ◽  
Class Of Functions

Let $F(b,M,n)$($b\neq 0$, complex, $M >1/2$, and $n$ is a positive integer) denote the classof functions $f(z)=z+\sum_{k=n+1}^\infty a_kz^k$ analytic in $U=\{z: |z|< 1\}$ which satisfy for fixed $M$, $f (z)/z \neq 0$ in $U$ and  \[ \left|\frac{b-1+\frac{zf'(z)}{f(z)}}{b}-M\right|<M, \quad z\in U.\] Also let $F^*(b,M,n)$ ($b\neq 0$, complex, $M >1/2$, and $n$ is a positive integer) denote the class of functions $f(z)=1/z+\sum_{k=n}^\infty a_kz^k$ analytic in the annulus $U^* = \{z : 0 < |z| < 1\}$ which satisfy \[ \left|\frac{b-1+\frac{zf'(z)}{f(z)}}{b}-M\right|<M, \quad z\in U^*.\] In this paper we obtain bounds for the coefficients of functions of the above classes.

scholarly journals On a Subclass of Analytic Functions That Are Starlike with Respect to a Boundary Point Involving Exponential Function

2022 ◽  
Vol 2022 ◽  
pp. 1-8
Author(s):  
Adam Lecko ◽  
Gangadharan Murugusundaramoorthy ◽  
Srikandan Sivasubramanian
Keyword(s):  
Exponential Function ◽  
Analytic Functions ◽  
Boundary Point ◽  
Unit Disc ◽  
Starlike Functions ◽  
Analytic Formula ◽  
Coefficient Estimates ◽  
New Class ◽  
Differential Subordinations ◽  
Class Of Functions

In the present exploration, the authors define and inspect a new class of functions that are regular in the unit disc D ≔ ς ∈ ℂ : ς < 1 , by using an adapted version of the interesting analytic formula offered by Robertson (unexploited) for starlike functions with respect to a boundary point by subordinating to an exponential function. Examples of some new subclasses are presented. Initial coefficient estimates are specified, and the familiar Fekete-Szegö inequality is obtained. Differential subordinations concerning these newly demarcated subclasses are also established.

scholarly journals A Class of Analytic Functions with Missing Coefficients

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Ding-Gong Yang ◽  
Jin-Lin Liu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Bounds ◽  
Radius Of Convexity ◽  
Convolution Properties ◽  
Class Of Functions

Let and denote the class of functions of the form which are analytic in the open unit disk and satisfy the following subordination condition , for, for. We obtain sharp bounds on , and coefficient estimates for functions belonging to the class . Conditions for univalency and starlikeness, convolution properties, and the radius of convexity are also considered.

scholarly journals Coefficient estimates for Ruscheweyh derivatives

2004 ◽  
Vol 2004 (36) ◽  
pp. 1937-1942 ◽  
Author(s):  
Maslina Darus ◽  
Ajab Akbarally
Keyword(s):  
Unit Disc ◽  
Upper Bounds ◽  
Coefficient Estimates ◽  
Class Of Functions

We consider functionsf, analytic in the unit disc and of the normalized formf(z)=z+∑n=2∞anzn. For functionsf∈R¯δ(β), the class of functions involving the Ruscheweyh derivatives operator, we give sharp upper bounds for the Fekete-Szegö functional|a3−μa22|.

scholarly journals On a class ofp-valent close-to-convex functions of orderβand typeα

1988 ◽  
Vol 11 (2) ◽  
pp. 259-266 ◽  
Author(s):  
M. K. Aouf
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Coefficient Estimates ◽  
Distortion Theorems ◽  
Class Of Functions

LetS(A,B,p,α)denote the class of functionsg(z)=zp+∑n=p+1∞bnznanalytic in the unit discU={z:|z|<1}and satisfying the conditionzg′(z)g(z)<p+[pB+(A−B)(p−α)]z1+Bz,   z∈U,   −1≦B<A≦1,   0≦α<p.LetC(A,B,p,β,α)denote the class of functionsf(z)=zp+∑n=p+1∞anznanalytic inU, and satisfying the conditionRe{zf′(z)g(z)}>β,  z∈U,   g∈S(A,B,p,α).In this paper we determine the coefficient estimates and distortion theorems for the classC(A,B,p,β,α).

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