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
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
In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with vary...In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.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 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
Making use of a multiplier transformation, which is defined by means of the Hadamard product (or convolution), we introduce some new subclasses of analytic functions and investigate their inclusion relationships and a...Making use of a multiplier transformation, which is defined by means of the Hadamard product (or convolution), we introduce some new subclasses of analytic functions and investigate their inclusion relationships and argument properties.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
In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent a-convex functions of complex order. These results extend some known theorems.
The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator. Differential sandwich-type theorems for these unival...The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator. Differential sandwich-type theorems for these univalent functions, and some consequences involving well-known special functions are also presented.展开更多
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.
基金supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge,University of Rzeszów
文摘In the paper we introduce an idea of harmonic functions with correlated coefficients which generalize the ideas of harmonic functions with negative coefficients introduced by Silverman and harmonic functions with varying coefficients defined by Jahangiri and Silverman. Next we define classes of harmonic functions with correlated coefficients in terms of generalized Dziok-Srivastava operator. By using extreme points theory, we obtain estimations of classical convex functionals on the defined classes of functions. Some applications of the main results are also considered.
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 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.
文摘Making use of a multiplier transformation, which is defined by means of the Hadamard product (or convolution), we introduce some new subclasses of analytic functions and investigate their inclusion relationships and argument properties.
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Foundation item： Supported by the Natural Science Foundation of Inner Mongolia（2009MS0113） Sup- ported by the Higher School Research Foundation of Inner Mongolia（NJzy08150）
文摘In this paper, we obtain the convexity of new general integral operator on some classes of k-uniformly p-valent a-convex functions of complex order. These results extend some known theorems.
文摘The authors obtain subordination and superordination preserving properties for a new defined generalized operator involving the Srivastava-Attiya integral operator. Differential sandwich-type theorems for these univalent functions, and some consequences involving well-known special functions are also presented.
