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1
Content available remote Length problems for Bazilevič functions
EN
Let C(r) denote the curve which is image of the circle |z|=r<1 under the mapping f. Let L(r) be the length of C(r) and A(r) the area enclosed by the curve C(r). Furthermore M(r) = max|z|=r |f(z)|. We present some relations between these notions for Bazilevič functions.
EN
We investigate the third Hankel determinant problem for some starlike functions in the open unit disc, that are related to shell-like curves and connected with Fibonacci numbers. For this, firstly, we prove a conjecture, posed in [17], for sharp upper bound of second Hankel determinant. In the sequel, we obtain another sharp coefficient bound which we apply in solving the problem of the third Hankel determinant for these functions.
EN
In this paper, we determine the coefficient estimates and the Fekete-Szegö inequalities for [wzór], the class of analytic and univalent functions associated with quasi-subordination.
4
EN
Some Ostrowski type inequalities for functions whose second derivatives in absolute value at certain powers are s-convex in the second sense are established. Two mistakes in a recently published paper are pointed out and corrected.
5
Content available remote Conditionally approximately convex functions
EN
Let X be a real normed space, V be a subset of X and α: [0, ∞) → [0, ∞) be a nondecreasing function. We say that a function f : V → [-∞, ∞) is conditionally α-convex if for each convex combination (…) of elements from V such that (…), the following inequality holds true (…). We present some necessary and some sufficient conditions for f to be conditionally α-convex.
EN
We define two new general integral operators for certain analytic functions in the unit disc U and give some sufficient conditions for these integral operators on some subclasses of analytic functions.
EN
Some new inequalities of the Ostrowski type for twice differentiable mappings whose derivatives in absolute value are s-convex in the second sense are given.
EN
The aim of this paper is to introduce two new classes of analytic function by using principle of subordination and the Dziok-Srivastava operator. We further investigate convolution properties for these calsses. We also nd necessary and sufficient condition and coefficient estimate for them.
9
Content available remote Applications of convolution properties
EN
K. I. Noor (2007 Appl. Math. Comput. 188, 814–823) has defined the classes Qk(a, b, λ, γ) and Tk(a, b, λ, γ) of analytic functions by means of linear operator connected with incomplete beta function. In this paper, we have extended some of the results and have given other properties concerning these classes.
10
Content available remote A class of univalent functions involving a differentio-integral operator
EN
This paper focuses on a generalized linear operator Im which is a combination of both differential and integral operators. Involving this operator, a class Tsk(...) with respect to k-symmetric points is defined. Results based on coefficient inequalities and bounds for this class are obtained. Various integral representations and some consequent results for TS(...) class are also determined. Further, results on partial sums are discussed.
EN
In this paper, we find the conditions on parameters a, b, c and q such that the basic hypergeometric function zφ(a,b;c;q,z) and its q-Alexander transform are close-to-convex (and hence univalent) in the unit disc D:={z: |z|<1}.
EN
In this paper, we introduce and investigate a new class of multivalent functions by using the Hadamard product structure defined in the open unit disk. We obtain coefficient estimates, a distortion theorem, extreme points and criteria of starlikeness and convexity for functions which belong to our class. Relevant connections of the results with those obtained in earlier works are also pointed out.
13
Content available remote Subclasses of univalent functions related with circular domains
EN
We investigate the family of functions normalized by the condition ƒ(0) = ƒ(0) - 1 = 0, that are analytic in the unit disk, with the property that the domain of values [...] is the disk |z-b| < b, b ≥ 1. Integral and convolution characterizations are found and coefficients bounds are given.
EN
In this paper using a differential operator, we define a new subclass of meromorphic functions. Sharp upper bounds for the functional […] in this class are obtained. An inclusion property is also given.
16
Content available remote On a certain class of analytic functions involving hypergeometric functions
EN
A certain class of functions analytic in the open unit disk and defined in terms of hypergeometric functions is introduced and investigated. We establish starlikeness, convexity and spirallikeness properties for this class of functions. Special cases and some useful consequences of our main results are aslo mentioned.
17
Content available remote Applications of a first order differential subordination for analytic functions
EN
In the paper, we define classes of analytic functions, in terms of subordination. By using Jack's Lemma and the Briot-Bouquet differential subordination we obtain some inclusion relations for defined classes.
18
Content available remote Subordinations and superordinations using the Dziok-Srivastava linear operator
EN
By using the properties of the Dziok-Srivastava linear operator we obtain differential subordinations and superordinations by using functions from class A. A sandwich-type result is also given. Theorem 1 from the paper gives sufficient conditions such that a function f ∈ A to be starlike, convex and α-convex.
EN
In the paper, we introduce a generalized class of k-starlike functions associated with Wright generalized hypergeometric functions and obtain the sequential subordination results and integral means inequalities. Some interesting consequences of our results are also pointed out.
EN
In the present paper we define a new operator using the Salagean and Ruscheweyh operators. Denote by L(m)(α) the operator given by [wzór], where R(m)f(z) denote the Ruscheweyh derivative, S(m)f(z) is the Salagean operator and [wzór] is the class of normalized analytic functions. A certain subclass, denoted by [wzór], of analytic functions in the open unit disc is introduced by means of the new operator. By making use of the concept of differential subordination we will derive various properties and characteristics of the class [wzór]. Also, several differential subordinations are established regardind the operator L(m)(α).
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