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1
Content available remote Coefficient inequalities for a subclass of Bazilevič functions
EN
Let f be analytic in D={z:|z| < 1} with f(z)=z+∑∞n=2anzn, and for α ≥ 0 and 0 < λ ≤ 1, let B1(α,λ) denote the subclass of Bazilevič functions satisfying (…) <λ for 0 < λ ≤ 1. We give sharp bounds for various coefficient problems when f ∈ B1(α,λ), thus extending recent work in the case λ = 1.
EN
In the paperwe discuss the functional Φf(μ) ≡ a2a4 − μa23 for functions in the class R(α), α ϵ [0, 1). This class consists of analytic functions which satisfy the condition Re f’ (z) > α for all z in the unit disk Δ.We show that the conjecture of Hayami and Owa [1], that is, |Φf(μ)| ≤ (1 − α)2 · max{ 1/2 – 4/9μ, 4/9μ} for all f ϵ R(α) and μ ϵ R, is false. Moreover, we find estimates of |Φf(μ)| that improve the results obtained by Hayami and Owa.
EN
In this paper, we introduce and investigate two new subclasses of the function class ∑ of bi-univalent functions defined in the open unit disk, which are associated with fractional q-calculus operators, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these new subclasses. Several (known or new) consequences of the results are also pointed out.
4
Content available remote New univalence criterions for special general integral operators
EN
In this work we consider some integral operators on the special subclasses of the set of analytic functions in the unit disc which are defined by the Hadamard product. Using the univalence criterions, we obtain new sucient conditions for these operators to be univalent in the open unit disk. We give some applications of the main results.
EN
The object of this paper is to derive some inclusion relations regarding a new class by using the generalized differential operator due to the authors.
EN
In this paper we introduce the class K(s,b,beta,apha) of analytic functions defined by the Srivastava-Attiya convolution operator Js,b(f) involving the Hurwitz-Lerch Zeta function. We derive few subordination results for the functions in the class K(s,b,beta,alpha) and discuss the interesting applications of subordination results with the help of convex functions. Several other properties like coefficient inequalities growth and distortion theorems, extreme points, integral mean inequalities, partial sums and quasi-Hadamard product are investigated for the class K(s,b,beta,alpha). The authors also obtain Fekete-Szego inequality for normalized analytic functions f(z) defined on the open unit disc for which [....] lies in a region starlike with respect to 1 and is symmetric with respect to the real axis. Applications of our main result involving the Owa-Srivastava operator of fractional calculus are discussed. Finally as one of the applications of our result, we derive the Fekete-Szego inequality for a class of normalized analytic functions, defined using the Hadamard product and the Owa-Srivastava operator.
EN
We study a correspondence L between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every ƒ and w ∈ H, exp(L(ƒ)(w)) = ƒ(exp w). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(H) of all univalent functions g on H for which = g(w) + 2 πi) = g(w) + 2 πi and limRe z →-- ∞(g(w) - w)=0.
EN
Let T be the class of functions f with negative coefficients which are analytic and univalent in the open disk U with f(0) = 0 and f'(0) = 1. For the classes T* (A, B) and C (A,B), -1 ≤ A < B ≤ 1 defined as subclasses of T, interesting results for integral means are discussed.
9
Content available remote On certain properties of neighborhoods of analytic functions of complex order
EN
Let A(n) denote the class of functions of the form [wzór] which are analytic in the open unit disk U = {z : |z| < 1}. In this note, the subclasses Sn (β, γ, a, c), Rn (β, γ, a, c; μ ), S(sup α) (sub n) (β, γ a, c) and R (sup α) (sub n) (β, γ, a, c; μ ) of A(n)(are defined and some properties of neighborhoods arę studied for functions of complex order in these classes.
EN
In our present work we obtained some interesting properties of convolution using the generalized Sâlâgean operator on univalent functions with rnissing coefficients, also we investigate other results by making use of subordination concept.
11
Content available remote On certain class of analytic functions associated with a convolution structure
EN
Making use of a convolution structure, we introduce a new class of analytic functions defined in the open unit disc and investigate its various characteristics. Apart from deriving a set of coefficient bounds, we establish several inclusion relation-ships involving the (n, [...)-neighborhoods of analytic functions with negative coefficients belonging to this subclass.
12
Content available remote On a subclass of uniformly convex functions with fixed second coefficient
EN
Using of Salagean operator, we define a new subclass of uniformly convex functions with negative coefficients and with fixed second coefficient. The main objective of this paper is to obtain coefficient estimates, distortion bounds, closure theorems and extreme points for functions belonging of this new class. The results are generalized to families with fixed finitely many coefficients.
EN
The authors establish certain results concerning the generalized Hadamard products of certain meromorphic univalent functions with positive coefficients analagous to the results due to Choi et al. (J. Math. Anal. Appl. 199(1996), 495-501).
14
Content available remote Functions convex in the positive direction of the imaginary axis
EN
The aim of this paper is to present a new method of the proof of an analytic characterization of functions convex in the positive direction of the imaginary axis.
EN
Let C denote the compIex pIane and Iet U denote the open unit disk. In this paper the second order nonlinear differential inequalities are investigated. Properties of the function which satisfies such differential inequalities are derived. Some applications in the theory of univalent function are presented.
16
Content available remote Univalence criterion for certain integral operators
EN
Pescar investigated the univalence of certain integral operators. We will show that the results are obtained by the Schwarz lemma. We will also give some generalizations.
17
Content available remote On the coefficients of a class of univalent functions
EN
We consider a class of univalent functions which verify a strong Milin type condition for logarithmic coefficients. This class contains all alfa-Koebe spirallike functions, all extremal points of the class of typically real functions, together with their rotations and multiplicative "compositions". We find some extremal functions of this class.
18
Content available remote On a problem H. S. Al-Amiri and M. O. Reade
EN
In the present paper, the authors investigate the univalence of the functions f, analytic in -E, f(O) = 0, f'(0) = 1 and which satisfy Re [(1 - alfa)f'(z) + alfa (1+ zf''(z): f'(z)] >beta, z is an element of E, where alfa > 0 and 0 < beta < 1. The univalence of such functions has already been established in the case when alfa < 0 and beta = 0 by H. S. Al-Amiri and M. 0. Reade in 1975.
19
Content available remote Linear invariance and integral operators of univalence functions
EN
In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains (1), where / belongs to the linear invariant family, and thereby we obtain information about the univalence of (1). In particular, we determine the order of this minimal invariant family in the cases of univalent and convex univalent functions in D. As a result, we find the radius of close-to-convexity and the lower bound for the radius of univalence for the minimal invariant family in the case of convex univalent functions. This allows us to determine the exact region for (a, (3) where the corresponding minimal invariant family is univalent and close-to-convex. These results are sharp and generalize those which were obtained in [11].
EN
In the aim of the present paper, two families of meromorphically multivalent (non-normalized) functions with complex coefficients in the punctured unit disk are stated. They also indicate relevant connections of these families of meromorphically multivalent and meromorphic univalent functions which involve some interesting results on this topics of Geometric and Analytic Functions Theory.
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