Huda al-Kharsani - Academia.edu (original) (raw)
Papers by Huda al-Kharsani
Tamkang Journal of …, 2006
... 273 Page 2. 274 RA AL-KHAL AND HA AL-KHARSANI ... In terms of Gamma functions, we are led to ... more ... 273 Page 2. 274 RA AL-KHAL AND HA AL-KHARSANI ... In terms of Gamma functions, we are led to the well-known Gauss's summation theorem: If Re(c − a − b) > 0, then F(a, b; c; 1) = Γ(c)Γ(c − a − b) Γ(c − a)Γ(c − b) , c = 0, −1, −2,... (1.6) ...
Journal of Inequalities in Pure and Applied Mathematics
The object of the present paper is to introduce a class of p−valent uniformly functions U CV p . ... more The object of the present paper is to introduce a class of p−valent uniformly functions U CV p . We deduce a criteria for functions to lie in the class U CV p and derive several interesting properties such as distortion inequalities and coefficients estimates. We confirm our results using the Mathematica program by drawing diagrams of extremal functions of this class.
Journal of Inequalities in Pure and Applied Mathematics
The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belongin... more The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belonging to the classes S *
Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics
Using the results of first order differential subordinations and superordinations, we define and ... more Using the results of first order differential subordinations and superordinations, we define and discuss new classes of p-valent functions involving the Dziok-Srivastava operator and multiplier transformation.
The purpose of the present paper is to derive superordination result for functions in the class M... more The purpose of the present paper is to derive superordination result for functions in the class M l,m µ (α, λ, b) of normalized analytic functions in the open unit disk U . A number of interesting applications of the superordination result are also considered.
Journal of Inequalities in Pure and Applied Mathematics
We use a parabolic region to prove certain inequalities for uniformly p-valent functions in the o... more We use a parabolic region to prove certain inequalities for uniformly p-valent functions in the open unit disk D.
Tamkang Journal of Mathematics
In terms of linear operators we introduce new classes of functions. Then by using differential su... more In terms of linear operators we introduce new classes of functions. Then by using differential subordinations, certain results concerning inclusion relations, coefficient bounds and other results are given.
Kyungpook Mathematical Journal
Let A(p) be the class of functions f : z p + ∞ j=1 ajz p+j analytic in the open unit disc E. Let,... more Let A(p) be the class of functions f : z p + ∞ j=1 ajz p+j analytic in the open unit disc E. Let, for any integer n > −p, fn+p−1
The purpose of the present paper is to obtain the sandwich-type theorem which contains the subord... more The purpose of the present paper is to obtain the sandwich-type theorem which contains the subordination-and superordination-preserving properties for certain integral operators defined on the space of normalized analytic functions in the open unit disk.
Let A denote the class of functions f(z)=z+∑ n=2 ∞ a n z n analytic and univalent in the unit dis... more Let A denote the class of functions f(z)=z+∑ n=2 ∞ a n z n analytic and univalent in the unit disk Δ and for α≥0, 0≤β<1 and 0<γ≤1 let S ¯ α,β * (γ) be the subclass of A consisting of such f that zf ' (z) f(z)≠β and arg(1-α)zf ' (z) f(z)+αz f ' (z) ' f ' (z)-β<γπ 2,(z∈Δ)· Results: 1. A function f from A belongs to S ¯ α,β * (γ) (a>0), if and only if f(z)=1 α∫ 0 z φ ( t ) 1 α dt t α for some φ from S ¯ 0,β * (γ), (which satisfy |arg(zφ ' (z) φ(z)-β)|<γπ 2, (z∈Δ).) 2. Sharp estimates on |a n |=|a n (f)|, f∈S ¯ α,β * (γ), n=2,3 as well as on |a 3 -μa 2 3 | (u∈R) are obtained.
Australian Journal of Mathematical Analysis and Applications
For given numbers α∈(0,1) and β∈(0,1), let S β * (γ) denote the class of funcions f(z)=z+∑ n=2 ∞ ... more For given numbers α∈(0,1) and β∈(0,1), let S β * (γ) denote the class of funcions f(z)=z+∑ n=2 ∞ a n z n , |z|<1, that satisfy the condition arg z(f(z)) ' f(z) - β<πγ 2· For f in S β * (γ) the authors gave a sharp upper bound for |a 4 | and determined the exact value of the radius of convexity. They also investigate some properties of integral or convolution operators.
Journal of Inequalities in Pure and Applied Mathematics
A necessary and sufficient coefficient is given for functions in a class of complex-valued harmon... more A necessary and sufficient coefficient is given for functions in a class of complex-valued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.
Let A be the class of functions f:f(z)=z+∑ n=2 ∞ a n z n analytic in the open unit disc U. Let q ... more Let A be the class of functions f:f(z)=z+∑ n=2 ∞ a n z n analytic in the open unit disc U. Let q f s (α 1 ,α 2 ,⋯,α 1 ;β 1 ,⋯,β s ;z)=∑ n=0 ∞ (α 1 ) n ⋯(α q ) n (β 1 )n⋯(β s ) n z n+1 n!(q≤s+1;q,s∈N 0 )· We define q f s (-1) (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z) by using convolution * as q f s (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z)* q f s (-1) (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z)=z/(1-z) 2 · We use this definition to introduce a generalized integral operator L q,s (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s )f(z)= q f s (-1) (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z)*f(z)· In terms of this integral operator we introduce new classes of functions and derive some interesting properties of these classes.
In this paper we introduce a class of strongly starlike func- tions of order and type with respec... more In this paper we introduce a class of strongly starlike func- tions of order and type with respect to symmetric points and investigate the neighborhoods and coecien ts bounds of such functions.
International Journal of Mathematics and Mathematical Sciences, 2008
Computers & Mathematics with Applications, 2010
ABSTRACT
For β < 1, n = 0, 1, 2, . . ., and −π < α ≤ π, we let M n (α, β) denote the family of functions f... more For β < 1, n = 0, 1, 2, . . ., and −π < α ≤ π, we let M n (α, β) denote the family of functions f (z) = z + · · · that are analytic in the unit disk and satisfy there the condition
Applied Mathematics and Computation, 2007
... Moreover, Miller and Mocanu [12] considered differential superordinations as the dual concept... more ... Moreover, Miller and Mocanu [12] considered differential superordinations as the dual concept of differential subordinations (see also [3], [4] and [17]). In the present paper, we obtain thesubordination-and superordination-preserving properties of the integral operator I β,γ ...
Tamkang Journal of …, 2006
... 273 Page 2. 274 RA AL-KHAL AND HA AL-KHARSANI ... In terms of Gamma functions, we are led to ... more ... 273 Page 2. 274 RA AL-KHAL AND HA AL-KHARSANI ... In terms of Gamma functions, we are led to the well-known Gauss's summation theorem: If Re(c − a − b) > 0, then F(a, b; c; 1) = Γ(c)Γ(c − a − b) Γ(c − a)Γ(c − b) , c = 0, −1, −2,... (1.6) ...
Journal of Inequalities in Pure and Applied Mathematics
The object of the present paper is to introduce a class of p−valent uniformly functions U CV p . ... more The object of the present paper is to introduce a class of p−valent uniformly functions U CV p . We deduce a criteria for functions to lie in the class U CV p and derive several interesting properties such as distortion inequalities and coefficients estimates. We confirm our results using the Mathematica program by drawing diagrams of extremal functions of this class.
Journal of Inequalities in Pure and Applied Mathematics
The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belongin... more The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belonging to the classes S *
Hacettepe University Bulletin of Natural Sciences and Engineering Series B: Mathematics and Statistics
Using the results of first order differential subordinations and superordinations, we define and ... more Using the results of first order differential subordinations and superordinations, we define and discuss new classes of p-valent functions involving the Dziok-Srivastava operator and multiplier transformation.
The purpose of the present paper is to derive superordination result for functions in the class M... more The purpose of the present paper is to derive superordination result for functions in the class M l,m µ (α, λ, b) of normalized analytic functions in the open unit disk U . A number of interesting applications of the superordination result are also considered.
Journal of Inequalities in Pure and Applied Mathematics
We use a parabolic region to prove certain inequalities for uniformly p-valent functions in the o... more We use a parabolic region to prove certain inequalities for uniformly p-valent functions in the open unit disk D.
Tamkang Journal of Mathematics
In terms of linear operators we introduce new classes of functions. Then by using differential su... more In terms of linear operators we introduce new classes of functions. Then by using differential subordinations, certain results concerning inclusion relations, coefficient bounds and other results are given.
Kyungpook Mathematical Journal
Let A(p) be the class of functions f : z p + ∞ j=1 ajz p+j analytic in the open unit disc E. Let,... more Let A(p) be the class of functions f : z p + ∞ j=1 ajz p+j analytic in the open unit disc E. Let, for any integer n > −p, fn+p−1
The purpose of the present paper is to obtain the sandwich-type theorem which contains the subord... more The purpose of the present paper is to obtain the sandwich-type theorem which contains the subordination-and superordination-preserving properties for certain integral operators defined on the space of normalized analytic functions in the open unit disk.
Let A denote the class of functions f(z)=z+∑ n=2 ∞ a n z n analytic and univalent in the unit dis... more Let A denote the class of functions f(z)=z+∑ n=2 ∞ a n z n analytic and univalent in the unit disk Δ and for α≥0, 0≤β<1 and 0<γ≤1 let S ¯ α,β * (γ) be the subclass of A consisting of such f that zf ' (z) f(z)≠β and arg(1-α)zf ' (z) f(z)+αz f ' (z) ' f ' (z)-β<γπ 2,(z∈Δ)· Results: 1. A function f from A belongs to S ¯ α,β * (γ) (a>0), if and only if f(z)=1 α∫ 0 z φ ( t ) 1 α dt t α for some φ from S ¯ 0,β * (γ), (which satisfy |arg(zφ ' (z) φ(z)-β)|<γπ 2, (z∈Δ).) 2. Sharp estimates on |a n |=|a n (f)|, f∈S ¯ α,β * (γ), n=2,3 as well as on |a 3 -μa 2 3 | (u∈R) are obtained.
Australian Journal of Mathematical Analysis and Applications
For given numbers α∈(0,1) and β∈(0,1), let S β * (γ) denote the class of funcions f(z)=z+∑ n=2 ∞ ... more For given numbers α∈(0,1) and β∈(0,1), let S β * (γ) denote the class of funcions f(z)=z+∑ n=2 ∞ a n z n , |z|<1, that satisfy the condition arg z(f(z)) ' f(z) - β<πγ 2· For f in S β * (γ) the authors gave a sharp upper bound for |a 4 | and determined the exact value of the radius of convexity. They also investigate some properties of integral or convolution operators.
Journal of Inequalities in Pure and Applied Mathematics
A necessary and sufficient coefficient is given for functions in a class of complex-valued harmon... more A necessary and sufficient coefficient is given for functions in a class of complex-valued harmonic univalent functions using the Dziok-Srivastava operator. Distortion bounds, extreme points, an integral operator, and a neighborhood of such functions are considered.
Let A be the class of functions f:f(z)=z+∑ n=2 ∞ a n z n analytic in the open unit disc U. Let q ... more Let A be the class of functions f:f(z)=z+∑ n=2 ∞ a n z n analytic in the open unit disc U. Let q f s (α 1 ,α 2 ,⋯,α 1 ;β 1 ,⋯,β s ;z)=∑ n=0 ∞ (α 1 ) n ⋯(α q ) n (β 1 )n⋯(β s ) n z n+1 n!(q≤s+1;q,s∈N 0 )· We define q f s (-1) (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z) by using convolution * as q f s (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z)* q f s (-1) (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z)=z/(1-z) 2 · We use this definition to introduce a generalized integral operator L q,s (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s )f(z)= q f s (-1) (α 1 ,α 2 ,⋯,α q ;β 1 ,⋯,β s ;z)*f(z)· In terms of this integral operator we introduce new classes of functions and derive some interesting properties of these classes.
In this paper we introduce a class of strongly starlike func- tions of order and type with respec... more In this paper we introduce a class of strongly starlike func- tions of order and type with respect to symmetric points and investigate the neighborhoods and coecien ts bounds of such functions.
International Journal of Mathematics and Mathematical Sciences, 2008
Computers & Mathematics with Applications, 2010
ABSTRACT
For β < 1, n = 0, 1, 2, . . ., and −π < α ≤ π, we let M n (α, β) denote the family of functions f... more For β < 1, n = 0, 1, 2, . . ., and −π < α ≤ π, we let M n (α, β) denote the family of functions f (z) = z + · · · that are analytic in the unit disk and satisfy there the condition
Applied Mathematics and Computation, 2007
... Moreover, Miller and Mocanu [12] considered differential superordinations as the dual concept... more ... Moreover, Miller and Mocanu [12] considered differential superordinations as the dual concept of differential subordinations (see also [3], [4] and [17]). In the present paper, we obtain thesubordination-and superordination-preserving properties of the integral operator I β,γ ...