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EN
In the class of analytic functions in the unit disc |z| < 1 we prove some new sufficient conditions for functions to be univalent or to be close-to-convex in the unit disc. Also we extend Ozaki’s condition that Re{exp(iα)f (p)(z)} > 0 in |z| < 1 implies that f(z) is at most p-valent in |z| < 1.
EN
We introduce an infinite-order linear differential operator and study its spectrum. We show that all analytical functions around the origin are its eigenfunctions corresponding to zero eigenvalue. We outline an interesting relation between this operator and the conservation law of energy in Hamiltonian mechanics.
3
The real and complex convexity
EN
We prove that the holomorphic differential equation ϕ’’(ϕ+c) = γ(ϕ’)² (ϕ:C→C be a holomorphic function and (γ, c) ϵ C²) plays a classical role on many problems of real and complex convexity. The condition exactly γ ϵ [wzór] (independently of the constant c) is of great importance in this paper. On the other hand, let n ≥ 1, (A₁, A₂) ϵ C² and g₁, g₂ : Cᵑ → C be two analytic functions. Put u(z, w) = │A ₁w - g₁(z) │² + │A₂w - g₂(z) │²v(z,w) = │A₁w - g₁(z) │² + │ A₂w - g₂(z) │², for (z,w) ϵ Cᵑ x C. We prove that u is strictly plurisubharmonic and convex on Cᵑ x C if and only if n = 1, (A₁, A₂) ϵ C² \{0} and the functions g₁ and g₂ have a classical representation form described in the present paper. Now v is convex and strictly psh on Cᵑ x C if and only if (A₁, A₂) ϵ C² \{0}, n ϵ {1,2} and and g₁, g₂ have several representations investigated in this paper.
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.
5
Cr-right equivalence of analytic functions
EN
Let f, g : (Rn , 0) → (R, 0) be analytic functions. We will show that if (…) and (…) then f and g are Cr-right equivalent, where (f) denoteideal generated by f and (…).
6
Fekete-Szego problem for certain subclasses of analytic functions
EN
In this present investigation, authors introduce certain subclasses of star like and convex functions of complex order b, using a linear multiplier differential operator (…). In this paper, for these classes the Fekete-Szegö problem is completely solved. Various new special cases of our results are also pointed out.
EN
In this paper, we further investigate the class of functions (…) which are analytic in the open unit disk (…),and involve the combinations of the representations of p-valently starlike and convex functions. We obtain several generalized results on the modified-Hadamard product of the class (…) which extend the corresponding results obtained by Altintas et al. [Computers Math. Applic. 30(2), 9-16, (1995)]; Darwish, Aouf [Mathematical and Computer Modelling (2007), doi:10.1016/j.mcm.2007.08.016 ]. Futher, by fixing the second coefficient of functions in (…) we introduce the special class (…) and discuss the extreme points.
8
A new class of multivalent analytic functions defined by the hadamard product
EN
The object of the present paper is to investigate the coefficients estimates, distortion properties, the radii of starlikeness and convexity, subordination theorems, partial sums and integral mean inequalities for classes of functions with two fixed points. Some remarks depicting consequences of the main results are also mentioned.
9
Generalized classes of uniformly convex functions
EN
In this paper we introduce some subclasses of analytic functions with varying argument of coeffcients. These classes are defined in terms of the Hadamard product and generalize the well-known classes of uniformly convex functions. We investigate the coeffcients estimates, distortion properties, radii of starlikeness and convexity for defined classes of functions.
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
In this paper we apply a fractional differintegral operator to a class of analytic functions and derive certain new sufficient conditions for the starlikeness of this class of functions. The usefulness of the main results are depicted by deducing several interesting corollaries and relevances with some of the earlier results are also pointed out.
EN
Using the Wright's generalized hypergeometric function, we introduce a new class Wk (p, q, s; A, B, lambda) of analytic p-valent functions with negative coefficients. In this paper we investigate coefficients estimates, distortion theorem, the radii of p-valent starlikeness and p-valent convexity and modified Hadamard products.
EN
In this paper, we obtain some applications of first order differential subordination and superordination results involving Dziok-Srivastava operator and other linear operators for certain normalized analytic functions in the open unit disk. The results, which are presented in this paper, have relevant connections with various previous results.
15
On an application of certain sufficient condition for starlikeness
EN
In this paper we consider a sufficient condition for furiction to be a-starlike function, when α ∈ [0, 1/2]. We use it for certain subclass of strongly starlike functions defined by a geometric condition. We take advantage of the techniąues of differential subordinations.
16
Classes of functions defined by subordination
EN
In the paper, we define classes of analytic functions, in terms of subordination. We present some inclusion relations for defined classes.
17
EN
In the present paper, we introduce a new subclass S(sup (j)) (sub p, λ) (α; a, c; φ) of multivalent functions involving the Cho-Kwon-Srivastava operator. Such results as inclusion relationships, coefficient estimates and convolution properties for this class are proved. The results presented here would provide extensions of those given in earlier works.
18
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.
19
On a subclass of p-valent functions
EN
In this paper we consider a subclass of p-valent functions defined by certain differential-integral operator. By using the Krein-Milman theorem we obtain the extreme points of the classs. Some extremal problems in the class are also determined.
EN
By making use of the familiar concept of neighbourhood of analytic and p-valent functions, the author prove coefficient bounds and distortion inequalities and associated inclusion relations for the (j, [...)-neighbourhoods of a family of p-valent functions with negative coefficients and defined by using Salagean operator which is defined by means of a certain non-homogenous Cauchy-Euler differential equation.
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