For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Feket...For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.展开更多
In this paper, we investigate the bounds of the coefficients of several classes of meromorphic bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors.
In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.
In this paper we consider the class of Bazilevic functions for bi-univalent functions. For this we will estimate the coefficients a2 and a3 using Caratheodory func- tions and the method of differential subordination.
In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a...In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.展开更多
In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell...In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?.展开更多
Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass of analytic and bi-univalent functions defined in the open unit disc U. Further, we fin...Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass of analytic and bi-univalent functions defined in the open unit disc U. Further, we find estimates on the coefficients and for functions in this subclass. Many relevant connections with known or new results are pointed out.展开更多
In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.
In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclas...In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclass. The results presented in this paper improve or generalize the recent works of other authors.展开更多
The main objective of this paper is to derive the upper bounds for the coefficients of functions in a subclass of analytic and bi-univalent functions associated with Faber polynomials. The consequences presented here ...The main objective of this paper is to derive the upper bounds for the coefficients of functions in a subclass of analytic and bi-univalent functions associated with Faber polynomials. The consequences presented here point out and correct the errors of some earlier results.展开更多
In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Fu...In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ｜a2｜ and ｜a3｜ for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several （known or new） consequences of the results are also pointed out.展开更多
In this paper, we investigate the coefficient estimate and Fekete-Szeg? inequality of a class of m-fold bi-univalent function defined by subordination. The results presented in this paper improve or generalize the rec...In this paper, we investigate the coefficient estimate and Fekete-Szeg? inequality of a class of m-fold bi-univalent function defined by subordination. The results presented in this paper improve or generalize the recent works of other authors.展开更多
In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient c...In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.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
The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson'...The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.展开更多
In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions o...In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.展开更多
Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈C:|z|<1}, normalized by the conditions f(0) = 0 and f'(0) = 1. Let U denote the set of all functions f ∈ A satisfying the conditio...Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈C:|z|<1}, normalized by the conditions f(0) = 0 and f'(0) = 1. Let U denote the set of all functions f ∈ A satisfying the condition |(z/f(z))^2f'(z)-1|<1 for z∈D.Let Ω be the class of all f∈A for which |zf'(z)-f(z)|<1/2, z∈D.In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.展开更多
In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence cr...In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence criteria depending on parameters.Anal.Math.Phys.,2014,4(1-2):23–34)is generalized.展开更多
Let SH be the class of functions f = h + ˉg that are harmonic univalent and sensepreserving in the open unit disk U = {z ∈ C : |z| < 1} for which f(0) = f′(0)-1 = 0. In the present paper, we introduce some new s...Let SH be the class of functions f = h + ˉg that are harmonic univalent and sensepreserving in the open unit disk U = {z ∈ C : |z| < 1} for which f(0) = f′(0)-1 = 0. In the present paper, we introduce some new subclasses of SH consisting of univalent and sensepreserving functions defined by convolution and subordination. Sufficient coefficient conditions,distortion bounds, extreme points and convolution properties for functions of these classes are obtained. Also, we discuss the radii of starlikeness and convexity.展开更多
In this paper, we estimate the Fekete-Szego functional with k-th root transform for the inverse of certain classes of analytic univalent functions using quasi-subordination.
文摘For the new subclass B of the bi-univalent functions constructed with the help of the(u,v)-Chebyshev polynomials of the second type,we get estimates for the first two initial coefficients and upper bounds of the Fekete-Szeg o functional.
基金Supported by the Natural Science Foundation of Anhui Provincial Department of Education(Grant Nos.KJ2018-A0833 KJ2018A0839)
文摘In this paper, we investigate the bounds of the coefficients of several classes of meromorphic bi-univalent functions. The results presented in this paper improve or generalize the recent works of other authors.
基金supported by NSFC(11071058)Educational Commission of Hubei Province of China(D2011006)
文摘In this paper, we investigate the bounds of the coefficients of several classes of bi-univalent functions. The results presented in this paper improve of generalize the recent works of other authors.
文摘In this paper we consider the class of Bazilevic functions for bi-univalent functions. For this we will estimate the coefficients a2 and a3 using Caratheodory func- tions and the method of differential subordination.
基金The NSF(KJ2015A372) of Anhui Provincial Department of Education
文摘In this paper, we introduce several new subclasses of the function class Σ of bi-univalent functions analytic in the open unit disc defined by convolution.Furthermore, we investigate the bounds of the coefficients |a2| and |a3| for functions in these new subclasses. The results presented in this paper improve or generalize the recent works of other authors.
文摘In this paper, we have investigated second Hankel determinants and FeketeSzeg? inequalities for some subclasses of Bi-univalent functions with respect to symmetric and Conjugate points which are subordinate to a shell shaped region in the open unit disc ?.
文摘Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass of analytic and bi-univalent functions defined in the open unit disc U. Further, we find estimates on the coefficients and for functions in this subclass. Many relevant connections with known or new results are pointed out.
基金The NSF(KJ2018A0839,KJ2018A0833) of Anhui Provincial Department of Education
文摘In this paper, we investigate the coefficient estimates of a class of m-fold bi-univalent function de?ned by subordination. The results presented in this paper improve or generalize the recent works of other authors.
基金The NSF(11561001)of Chinathe NSF(2014MS0101)of Inner Mongolia Province+1 种基金the Higher School Foundation(NJZY19211)of Inner Mongolia of Chinathe NSF(KJ2018A0839,KJ2018A0833)of Anhui Provincial Department of Education
文摘In this paper, we introduce a new subclass of bi-univalent functions defined by quasi-subordination and Hohlov operator and obtain the coefficient estimates and Fekete-Szego inequality for function in this new subclass. The results presented in this paper improve or generalize the recent works of other authors.
基金Supported by the National Natural Science Foundation of China(Grant No.11401041)
文摘The main objective of this paper is to derive the upper bounds for the coefficients of functions in a subclass of analytic and bi-univalent functions associated with Faber polynomials. The consequences presented here point out and correct the errors of some earlier results.
文摘In this paper, we introduce and investigate a new subclass of the function class ∑. of bi-univalent functions of the Mocanu-convex type defined in the open unit disk, satisfy Ma and Minda subordination conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients ｜a2｜ and ｜a3｜ for functions in the new subclass introduced here. Further Application of Hohlov operator to this class is obtained. Several （known or new） consequences of the results are also pointed out.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1156100111271045)+4 种基金the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT-18-A14)the Natural Science Foundation of Inner Mongolia of China(Grant No.2018MS01026)the Higher School Foundation of Inner Mongolia of China(Grant No.NJZY19211)the Natural Science Foundation of Anhui Provincial Department of Education(Grant Nos.KJ2018A0833 KJ2018A0839)
文摘In this paper, we investigate the coefficient estimate and Fekete-Szeg? inequality of a class of m-fold bi-univalent function defined by subordination. The results presented in this paper improve or generalize the recent works of other authors.
基金Supported by the Natural Science Foundation of Inner Mongolia Autonomous Region(Grant No.2019MS01023)the Research Program of Science and Technology at Universities of Inner Mongolia Autonomous Region(Grant Nos.NJZZ19209,NJZY20198).
文摘In this paper,we introduce certain subclasses of harmonic univalent functions associated with the Janowski functions,which are defined by using generalized(p,q)-post quantum calculus operators.Sufficient coefficient conditions,extreme points,distortion bounds and partial sums properties for the functions belonging to the subclasses are obtained.
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The present article is an account of results on univalent functions in multiply connected domains obtained by the author. It contains two rery simple proofs of Villat's formula; Schwarz's formula, Poisson's formula and Poisson-Jensen formula in multiply connected domains; the differentiability theorem with respect to the parameter of analytic function family containing one parametric variable on multiply connected domains; variation theorem and parametric representation theorem of univalent functions in multiply connected domains; the solution of an extremal problem of differentiable functionals.
基金Supported by the National Natural Science Foundation of China(Grant No.11401186)the Research Fund from Engineering and Technology College Yangtze University(Grant No.15J0802)
文摘In this paper, a new subclass N_Σ^（h,p）（m, λ, μ） of analytic and bi-univalent functions in the open unit disk U is defined by salagean operator. We obtain coefficients bounds ｜a_2｜ and ｜a_3｜ for functions of the class. Moreover, we verify Brannan and Clunie＇s conjecture ｜a_2｜ ≤2^（1/2）for some of our classes. The results in this paper extend many results recently researched by many authors.
基金supported by the Key Laboratory of Applied Mathematics in Hubei Province,Chinasupported by MNZZS(ON174017,Serbia)
文摘Let A denote the family of all analytic functions f(z) in the unit disk D={z ∈C:|z|<1}, normalized by the conditions f(0) = 0 and f'(0) = 1. Let U denote the set of all functions f ∈ A satisfying the condition |(z/f(z))^2f'(z)-1|<1 for z∈D.Let Ω be the class of all f∈A for which |zf'(z)-f(z)|<1/2, z∈D.In this paper, the relations between the two classes are discussed. Furthermore, some new results on the class Ω are obtained.
基金The NSF(11501001)of Chinathe NSF(1908085MA18)of Anhui Provincethe Foundation(Y01002428)of Anhui University
文摘In this paper,some new criteria for univalence of analytic functions defined in the unit disk in terms of two parameters are presented.Moreover,the related result of Aharonov and Elias(Aharonov D,Elias U.Univalence criteria depending on parameters.Anal.Math.Phys.,2014,4(1-2):23–34)is generalized.
基金Supported by the National Natural Science Foundation of China(Grant No.11561001)the Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region(Grant No.NJYT-18-A14)+1 种基金the Natural Science Foundation of Inner Mongolia Province(Grant Nos.2014MS0101 2018MS01026)
文摘Let SH be the class of functions f = h + ˉg that are harmonic univalent and sensepreserving in the open unit disk U = {z ∈ C : |z| < 1} for which f(0) = f′(0)-1 = 0. In the present paper, we introduce some new subclasses of SH consisting of univalent and sensepreserving functions defined by convolution and subordination. Sufficient coefficient conditions,distortion bounds, extreme points and convolution properties for functions of these classes are obtained. Also, we discuss the radii of starlikeness and convexity.
基金Supported by the National Natural Science Foundation of China (Grant No. 11561001)the Natural Science Foundation of Inner Mongolia of China (Grant No. 2018MS01026)+4 种基金the Natural Science Foundation of Anhui Provincial Department of Education (Grant Nos. KJ2018A0833KJ2020A0993KJ2020ZD74)Provincial Quality Engineering Project of Anhui Colleges and Universities (Grant No. 2018mooc608)the Key Cultivated Project at School Level of the National Science Fund of Guangzhou Civil Aviation College (Grant No. 18X0428)。
文摘In this paper, we estimate the Fekete-Szego functional with k-th root transform for the inverse of certain classes of analytic univalent functions using quasi-subordination.
