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
The aim of this paper is to establish the Fekete-Szego inequality for a subclass of bi-univalent strongly quasi-starlike functions which is defined in the open unit disk. Furthermore, the coefficients a2 and a3 for fu...The aim of this paper is to establish the Fekete-Szego inequality for a subclass of bi-univalent strongly quasi-starlike functions which is defined in the open unit disk. Furthermore, the coefficients a2 and a3 for functions in this new subclass are estimated.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.
Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S ...Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.展开更多
In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established.Integral transforms of functions in these classes are also considered.In parti...In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established.Integral transforms of functions in these classes are also considered.In particular,our results include of improve several results due to Mogra et al.[2],Mogra [3],Goel and Sohe [4] and Bajpai[5].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
In this paper, using Salagean differential operator, we define and investigate a new subclass of univalent functions . We also establish a characterization property for functions belonging to the class .
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
A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined e...A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.展开更多
In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by ...In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.展开更多
The concept of quasi-periodic property of a function has been introduced by Harald Bohr in 1921 and it roughly means that the function comes (quasi)-periodically as close as we want on every vertical line to the value...The concept of quasi-periodic property of a function has been introduced by Harald Bohr in 1921 and it roughly means that the function comes (quasi)-periodically as close as we want on every vertical line to the value taken by it at any point belonging to that line and a bounded domain Ω. He proved that the functions defined by ordinary Dirichlet series are quasi-periodic in their half plane of uniform convergence. We realized that the existence of the domain Ω is not necessary and that the quasi-periodicity is related to the denseness property of those functions which we have studied in a previous paper. Hence, the purpose of our research was to prove these two facts. We succeeded to fulfill this task and more. Namely, we dealt with the quasi-periodicity of general Dirichlet series by using geometric tools perfected by us in a series of previous projects. The concept has been applied to the whole complex plane (not only to the half plane of uniform convergence) for series which can be continued to meromorphic functions in that plane. The question arise: in what conditions such a continuation is possible? There are known examples of Dirichlet series which cannot be continued across the convergence line, yet there are no simple conditions under which such a continuation is possible. We succeeded to find a very natural one.展开更多
One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deri...One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.展开更多
Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition fo...Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.展开更多
n this paper, a new certain class of p-valent analytic functions with quasi-subordination is defined and the Fekete-Szeg5 problems for functions belonging to the classare derived. The results presented here provide ex...n this paper, a new certain class of p-valent analytic functions with quasi-subordination is defined and the Fekete-Szeg5 problems for functions belonging to the classare derived. The results presented here provide extensions of those given in some earlierworks.展开更多
In this paper, we considered the equality problem of weighted Bajraktarević means with weighted quasi-arithmetic means. Using the method of substituting for functions, we first transform the equality problem into solv...In this paper, we considered the equality problem of weighted Bajraktarević means with weighted quasi-arithmetic means. Using the method of substituting for functions, we first transform the equality problem into solving an equivalent functional equation. We obtain the necessary and sufficient conditions for the equality equation.展开更多
In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, t...In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.展开更多
According to the quasi paraboloid rule, a computer program was developed and the Gibbs free energy functions of some compounds in Sialon system were assessed and predicted. It makes the theoretical design of the Sial...According to the quasi paraboloid rule, a computer program was developed and the Gibbs free energy functions of some compounds in Sialon system were assessed and predicted. It makes the theoretical design of the Sialon materials possible.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 this paper,we obtain the convexity of new general integral operator on some classes of fc-uniformly p-valentα-convex functions of complex order.These results extend some known theorems.
We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized...We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.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.
基金The NSF(KJ2018A0833)of Anhui Provincial Department of Educationthe Scientific Research Foundation(17X0413)of Guangzhou Civil Aviation College
文摘The aim of this paper is to establish the Fekete-Szego inequality for a subclass of bi-univalent strongly quasi-starlike functions which is defined in the open unit disk. Furthermore, the coefficients a2 and a3 for functions in this new subclass are estimated.
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Denote S to be the class of functions which are analytic,normalized and univalent in the open unit disk U={z:|z|<1}.The important subclasses of S are the class of starlike and convex functions,which we denote by S and C.In this paper,we obtain the third Hankel determinant for the inverse of functions f(z)=z+∞Σn=2 anz^n belonging to S^*and C.
文摘In this paper we introduce and study some new subclasses of meromorphic starlike multivalent functions.Inclusion relations are established.Integral transforms of functions in these classes are also considered.In particular,our results include of improve several results due to Mogra et al.[2],Mogra [3],Goel and Sohe [4] and Bajpai[5].
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In this paper, using Salagean differential operator, we define and investigate a new subclass of univalent functions . We also establish a characterization property for functions belonging to the class .
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A Riesz space K1 whose elements are pairs of convex-set collections is presented for the study on the calculus of generalized quasi-differentiable functions. The space K1 is constructed by introducing a well-defined equivalence relation among pairs of collections of convex sets. Some important properties on the norm and operations in K1 are given.
文摘In this paper,a new quasi-interpolation with radial basis functions which satis- fies quadratic polynomial reproduction is constructed on the infinite set of equally spaced data.A new basis function is constructed by making convolution integral with a constructed spline and a given radial basis function.In particular,for twicely differ- entiable function the proposed method provides better approximation and also takes care of derivatives approximation.
文摘The concept of quasi-periodic property of a function has been introduced by Harald Bohr in 1921 and it roughly means that the function comes (quasi)-periodically as close as we want on every vertical line to the value taken by it at any point belonging to that line and a bounded domain Ω. He proved that the functions defined by ordinary Dirichlet series are quasi-periodic in their half plane of uniform convergence. We realized that the existence of the domain Ω is not necessary and that the quasi-periodicity is related to the denseness property of those functions which we have studied in a previous paper. Hence, the purpose of our research was to prove these two facts. We succeeded to fulfill this task and more. Namely, we dealt with the quasi-periodicity of general Dirichlet series by using geometric tools perfected by us in a series of previous projects. The concept has been applied to the whole complex plane (not only to the half plane of uniform convergence) for series which can be continued to meromorphic functions in that plane. The question arise: in what conditions such a continuation is possible? There are known examples of Dirichlet series which cannot be continued across the convergence line, yet there are no simple conditions under which such a continuation is possible. We succeeded to find a very natural one.
文摘One of the classical approaches in the analysis of a variational inequality problem is to transform it into an equivalent optimization problem via the notion of gap function. The gap functions are useful tools in deriving the error bounds which provide an estimated distance between a specific point and the exact solution of variational inequality problem. In this paper, we follow a similar approach for set-valued vector quasi variational inequality problems and define the gap functions based on scalarization scheme as well as the one with no scalar parameter. The error bounds results are obtained under fixed point symmetric and locally α-Holder assumptions on the set-valued map describing the domain of solution space of a set-valued vector quasi variational inequality problem.
基金Supported by the National Natural Science Foundation of China(11271293)
文摘Some common fixed point results for mappings satisfying a quasi-contractive condition which involves altering distance functions are obtained in partially ordered complete cone metric spaces. A sufficient condition for the uniqueness of common fixed point is proved. Also, an example is given to support our results.
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.2014MS0101)the Higher School Foundation of Inner Mongolia of China(Grant No.2015NJZY240,Grant No.2016NJZY251)
文摘n this paper, a new certain class of p-valent analytic functions with quasi-subordination is defined and the Fekete-Szeg5 problems for functions belonging to the classare derived. The results presented here provide extensions of those given in some earlierworks.
文摘In this paper, we considered the equality problem of weighted Bajraktarević means with weighted quasi-arithmetic means. Using the method of substituting for functions, we first transform the equality problem into solving an equivalent functional equation. We obtain the necessary and sufficient conditions for the equality equation.
文摘In this article, we propose by using the Hausdorff distance Simpson’s rule for the triple integral of a fuzzy-valued function and the error bound of this method, one of the variables of which is fuzzy. In addition, thin δ-fine partitions are introduced. The integration domain is a quasi-fuzzy parallelipiped. A numerical example is presented in order to show the application and the significance of the method.
文摘According to the quasi paraboloid rule, a computer program was developed and the Gibbs free energy functions of some compounds in Sialon system were assessed and predicted. It makes the theoretical design of the Sialon materials possible.
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.
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 fc-uniformly p-valentα-convex functions of complex order.These results extend some known theorems.
文摘We introduce a new class of complex valued harmonic functions associated with Wright hypergeometric functions which are orientation preserving and univalent in the open unit disc. Further we define, Wright generalized operator on harmonic function and investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.