Let A p(n)(p, n∈N={1,2,…}) denote the class of functions of the form f(z)=z p+a p+n z p+n +… which are analytic in the unit disc E={z:|z|<1}. By using the method of differential subordinati ons we give som...Let A p(n)(p, n∈N={1,2,…}) denote the class of functions of the form f(z)=z p+a p+n z p+n +… which are analytic in the unit disc E={z:|z|<1}. By using the method of differential subordinati ons we give some sufficient conditions for a function f(z)∈A p(n) to be a certain subclass R p(n,k) of p-valently close-to-convexity funct ions.展开更多
An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,...An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re {eiδ(1-z)2f′(z)} 〉 0, z ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.展开更多
In this paper, we define some new subclasses of strongly close-to-star and strongly close-to-convex p-valent functions defined in the open unit disc by using a differential operator. Some inclusion results, convolutio...In this paper, we define some new subclasses of strongly close-to-star and strongly close-to-convex p-valent functions defined in the open unit disc by using a differential operator. Some inclusion results, convolution properties are studied.展开更多
By applying the q-derivative, we introduce two new subclasses of p-valent functions with positive coefficients. By means of the well-known Jack’s lemma, some inequalities related to starlike, convex and close-to-conv...By applying the q-derivative, we introduce two new subclasses of p-valent functions with positive coefficients. By means of the well-known Jack’s lemma, some inequalities related to starlike, convex and close-to-convex functions are also obtained.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
Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2)...Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2) such that Re{e^iδ zf′(z)/hα(z)} 〉 0, z ∈ D. For the class l(hα) of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied.展开更多
In the present paper a class of extended close-to-convex functions Qk,λ(α,β,ρ) defined by making use of Ruscheweyh derivatives is introduced and studied. We provide integral representations, distortion theorem, ra...In the present paper a class of extended close-to-convex functions Qk,λ(α,β,ρ) defined by making use of Ruscheweyh derivatives is introduced and studied. We provide integral representations, distortion theorem, radius of close-to-convexity and Hadamard product properties for this class.展开更多
文摘Let A p(n)(p, n∈N={1,2,…}) denote the class of functions of the form f(z)=z p+a p+n z p+n +… which are analytic in the unit disc E={z:|z|<1}. By using the method of differential subordinati ons we give some sufficient conditions for a function f(z)∈A p(n) to be a certain subclass R p(n,k) of p-valently close-to-convexity funct ions.
文摘An analytic function f in the unit disk D := {z ∈ C : |z| 〈 1}, standardly normalized, is called close-to-convex with respect to the Koebe function k(z) := z/(1-z)2, z ∈ D, if there exists δ ∈ (-π/2,π/2) such that Re {eiδ(1-z)2f′(z)} 〉 0, z ∈ D. For the class C(k) of all close-to-convex functions with respect to k, related to the class of functions convex in the positive direction of the imaginary axis, the Fekete-Szego problem is studied.
文摘In this paper, we define some new subclasses of strongly close-to-star and strongly close-to-convex p-valent functions defined in the open unit disc by using a differential operator. Some inclusion results, convolution properties are studied.
文摘By applying the q-derivative, we introduce two new subclasses of p-valent functions with positive coefficients. By means of the well-known Jack’s lemma, some inequalities related to starlike, convex and close-to-convex functions are also obtained.
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Given α∈[0, 1], let hα(z) := z/(1 - αz), z ∈ D := {z ∈ C: |z| 〈 1}. An analytic standardly normalized function f in D is called close-to-convex with respect to hα if there exists δ ∈ (-π/2, π/2) such that Re{e^iδ zf′(z)/hα(z)} 〉 0, z ∈ D. For the class l(hα) of all close-to-convex functions with respect to hα, the Fekete-Szego problem is studied.
基金the Natural Science Foundation of Inner Mongolia (No.2009MS0113)Higher School Research Foundation of Inner Mongolia (No.NJzy08510)
文摘In the present paper a class of extended close-to-convex functions Qk,λ(α,β,ρ) defined by making use of Ruscheweyh derivatives is introduced and studied. We provide integral representations, distortion theorem, radius of close-to-convexity and Hadamard product properties for this class.