In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known clas...In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known classes of functions defined by linear operators are also considered.展开更多
Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f i...Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.展开更多
In this paper, we consider a new class CS＊s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function φ（z, s, a）. Basi...In this paper, we consider a new class CS＊s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function φ（z, s, a）. Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.展开更多
In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the...M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.展开更多
We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,an...We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.展开更多
This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（...This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（z）＋（1-α）zf＇（z）/f（z）∈p（U）for all z ∈ U, where αis a real number and p（z）=1＋r^2z^2/1-Tz-T^2z^2（z∈ U）. The number T = （1 -√5）/2 is such that T^2 = 1 ＋ T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 （2011）, 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.展开更多
Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1...Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1）.Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0and｜zf＇（z）-f（z）｜〈1/2（｜z｜〈1）.In this article,we discuss the properties of U and Ω.展开更多
In the present investigation we define a new class of meromorphic functions on the punctured unit disk A△^＊ ：= {z ∈ C ： 0 〈 ｜z｜ 〈 1} by making use of the generalized Dziok-Srivastava operator Hm^l [α1]. Coef...In the present investigation we define a new class of meromorphic functions on the punctured unit disk A△^＊ ：= {z ∈ C ： 0 〈 ｜z｜ 〈 1} by making use of the generalized Dziok-Srivastava operator Hm^l [α1]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.展开更多
By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1...By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1 + α{1 +z[_lI_mf(z)]′′/[_lI_mf(z)]′}/z[_lI_mf(z)]′/_lI_mf(z))■φ(z)(α ∈ C-{1/2, 1}).展开更多
In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a corr...In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.展开更多
For real parameters αand β such that 0≤α 〈 1 〈β, we denote by S（α,β） the class of normalized analytic functions which satisfy the following two-sided inequality：where U denotes the open unit disk. We find ...For real parameters αand β such that 0≤α 〈 1 〈β, we denote by S（α,β） the class of normalized analytic functions which satisfy the following two-sided inequality：where U denotes the open unit disk. We find a sufficient condition for functions to be in the class S（α,β） and solve several radius problems related to other well-known function classes.展开更多
Let D_(r):={z=x+iy∈C:|z|<r},r≤1.For a normalized analytic function f in the unit disk D:=D1,estimating the Dirichlet integralΔ(r,f)=∫∫_(D_(r))|f'(z)|^(2) dxdy,z=x+iy,is an important classical problem in co...Let D_(r):={z=x+iy∈C:|z|<r},r≤1.For a normalized analytic function f in the unit disk D:=D1,estimating the Dirichlet integralΔ(r,f)=∫∫_(D_(r))|f'(z)|^(2) dxdy,z=x+iy,is an important classical problem in complex analysis.Geometrically,Δ(r,f)represents the area of the image of D_(r)under f counting multiplicities.In this paper,our main ob jective is to estimate areas of images of D_(r)under non-vanishing analytic functions of the form(z/f)^(μ),μ>0,in principal powers,when f ranges over certain classes of analytic and univalent functions in D.展开更多
文摘In the paper we investigate convolution properties related to the prestarlike functions and various inclusion relationships between defined classes of functions. Interest-ing applications involving the well-known classes of functions defined by linear operators are also considered.
基金supported by the Grant No.20-16367/NRPU/RD/HEC/20212021。
文摘Let q_(λ)(z)=1+λsinh(ζ),0<λ<1/sinh(1)be a non-vanishing analytic function in the open unit disk.We introduce a subclass S^(*)(q_(λ))of starlike functions which contains the functions f such that zf'/f is subordinated by q_(λ).We establish inclusion and radii results for the class S^(*)(q_(λ))for several known classes of starlike functions.Furthermore,we obtain sharp coefficient bounds and sharp Hankel determinants of order two for the class S^(*)(q_(λ)).We also find a sharp bound for the third Hankel determinant for the caseλ=1/2.
文摘In this paper, we consider a new class CS＊s,b of generalized close-to-starlike functions, which is defined by means of the Srivastava-Attiya operator Js,b involving the Hurwitz-Lerch Zeta function φ（z, s, a）. Basic results such as inclusion relations, coefficient inequalities and other interesting properties of this class are investigated. Relevant connections of some of the results presented here with those that were obtained in earlier investigations are pointed out briefly.
文摘In this paper we derive certain sufficient conditions for starlikeness and convexity of order α of meromorphically multivalent functions in the punctured unit disk.
基金This research was supported by NNSF of China(Grant No.10231040)NCET(06-0504)
文摘M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.
文摘We investigate some new subclasses of analytic functions of Janowski type of complex order.We also study inclusion properties,distortion theorems,coefficient bounds and radius of convexity of the functions.Moreover,analytic properties of these classes under certain integral operator are also discussed.Our findings are more comprehensive than the existing results in the literature.
文摘This article presents some new results on the class SLMα of functions that are analytic in the open unit disc U = {z ： ｜z｜〈 1} satisfying the conditions that f（0） =0, f＇（0）= 1, and α（1＋zf＇＇（z）/f＇（z）＋（1-α）zf＇（z）/f（z）∈p（U）for all z ∈ U, where αis a real number and p（z）=1＋r^2z^2/1-Tz-T^2z^2（z∈ U）. The number T = （1 -√5）/2 is such that T^2 = 1 ＋ T. The class SFLMa introduced by J. Dziok, R.K. Raina, and J. Sokot [3, Appl. Math. Comput. 218 （2011）, 996-1002] is closely related to the classes of starlike and convex functions. The article deals with several ideas and techniques used in geometric function theory and differential subordinations theory.
基金Supported by the Key Laboratory of Applied Mathematics in Hubei Province,China
文摘Let A be the space of functions analytic in the unit disk D = {z：｜z｜ 〈 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0 and｜f＇（z）（z/f（z））2-1｜〈1（｜z｜〈1）.Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f（0） = f＇（0）-1 = 0and｜zf＇（z）-f（z）｜〈1/2（｜z｜〈1）.In this article,we discuss the properties of U and Ω.
文摘In the present investigation we define a new class of meromorphic functions on the punctured unit disk A△^＊ ：= {z ∈ C ： 0 〈 ｜z｜ 〈 1} by making use of the generalized Dziok-Srivastava operator Hm^l [α1]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.
基金The NSF(KJ2015A372)of Anhui Provincial Department of Education
文摘By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1 + α{1 +z[_lI_mf(z)]′′/[_lI_mf(z)]′}/z[_lI_mf(z)]′/_lI_mf(z))■φ(z)(α ∈ C-{1/2, 1}).
文摘In the present paper, we study certain differential inequalities involving p-valent functions and obtain sufficient conditions for uniformly p-valent starlikeness and uniformly p-valent convexity. We also offer a correct version of some known criteria for uniformly p-valent starlike and uniformly p-valent convex functions.
文摘For real parameters αand β such that 0≤α 〈 1 〈β, we denote by S（α,β） the class of normalized analytic functions which satisfy the following two-sided inequality：where U denotes the open unit disk. We find a sufficient condition for functions to be in the class S（α,β） and solve several radius problems related to other well-known function classes.
文摘Let D_(r):={z=x+iy∈C:|z|<r},r≤1.For a normalized analytic function f in the unit disk D:=D1,estimating the Dirichlet integralΔ(r,f)=∫∫_(D_(r))|f'(z)|^(2) dxdy,z=x+iy,is an important classical problem in complex analysis.Geometrically,Δ(r,f)represents the area of the image of D_(r)under f counting multiplicities.In this paper,our main ob jective is to estimate areas of images of D_(r)under non-vanishing analytic functions of the form(z/f)^(μ),μ>0,in principal powers,when f ranges over certain classes of analytic and univalent functions in D.
