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1

On q-analogue of Janowski-type starlike functions with respect to symmetric points

Khan Muhammad Ghaffar, Ahmad Bakhtiar, Khan Raees, Zubair Muhammad, Salleh Zabidin

Demonstratio Mathematica

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2021

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Vol. 54, nr 1

37--46

EN

The main objective of the present paper is to define a class of q-starlike functions with respect to symmetric points in circular domain. Some interesting results of these functions have been evaluated in this article. The sufficiency criteria in the form of convolutions are evaluated. Furthermore, other geometric properties such as coefficient bounds, distortion theorem, closure theorem and extreme point theorem are also obtained for these newly defined functions.

2

Radius problems for univalent functions

Sokół Janusz, Trąbka-Więcław Katarzyna

Journal of Applied Analysis

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2020

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Vol. 26, nr 1

111--115

EN

This paper considers the following problem: for what value r, r < 1 a function that is univalent in the unit disk |z| < 1 and convex in the disk |z| < r becomes starlike in |z| < 1. The number r is called the radius of convexity sufficient for starlikeness in the class of univalent functions. Several related problems are also considered.

3

The order of starlikeness of uniformly convex functions

Wiśniowska-Wajnryb A.

Journal of Applied Analysis

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2017

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Vol. 23, nr 1

33--38

EN

We investigate classes of k-uniformly convex functions which generalize the class UCV introduced by Goodman in 1991. We solve the problem of finding the largest α ≥ 0 such that the class of k-uniformly convex functions is contained in the class of starlike functions of order α.

4

On Janowski harmonic functions

Dziok J.

Journal of Applied Analysis

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2015

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Vol. 21, nr 2

99--107

EN

In this paper we define classes of harmonic functions related to the Janowski functions and we give some necessary and sufficient conditions for these classes. Some topological properties and extreme points of the classes are also considered. By using extreme points theory we obtain coefficients estimates, distortion theorems, integral mean inequalities for the classes of functions.

5

On classes of meromorphic or complex harmonic functions with a pole at the infinity

Jakubowski Z., Sibelska A.

Demonstratio Mathematica

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2009

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Vol. 42, nr 3

479-489

EN

In this article we investigate some classes of meromorphic or complex harmonie functions with a pole, which are generated either by analytic conditions or by "coefficient inequalities". There are given theorems, which combine the geometrical properties of functions of the introduced classes. Some results broaden knowledge about the classes of functions, which were investigated in [15]. The main inspiration for the reaserch were the papers [4] and [11]. The part of results were presented in the XII-th International Mathematically-Informatical Conference in Chełm (2nd-5th July, 2006) [12].

6

Some properties of a subclass of uniformly convex functions with negative coefficients

Aouf M., Mostafa A.

Demonstratio Mathematica

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2008

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Vol. 41, nr 2

353-370

EN

The aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass TSlambda (n,alpha, beta) of uniformly convex functions with negative coefficients. We also derive many results for the modified Hadamard products of functions belonging to the class TSlambda(n,alpha, beta), and obtain several interesting distortion theorems for certain fractional operators of functions in this class. Finally, we consider integral operators associated with functions in this class.

7

On partial sums of certain analytic functions

Mostafa A.

Demonstratio Mathematica

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2008

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Vol. 41, nr 4

779-789

EN

In the present paper we give some results concerning partial sums of certain analytic functions analogous to the results due to H. Silverman [J. Math. Anal. Appl. 209 (1997), 221-227]. All the results are sharp.

8

Certain sufficienty conditions on Fox-Wright function

Chaurasia V., Parihar H.

Demonstratio Mathematica

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2008

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Vol. 41, nr 4

813-822

EN

The main object of this paper is to find certain conditions for the function [...] to be a member of certain subclasses of analytic functions. Our results provides generalization of some recent results due to Swaminathan [19] and Chaurasia and Srivastava [20].

9

Some relations including various linear operators

Dziok J.

Demonstratio Mathematica

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2007

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Vol. 40, nr 1

77-84

EN

Making use of the Carlson-Schaer linear operator, some subclasses of analytic functions are studied. Some relations including various linear operators are given.

10

On certain subclasses of p-valently analytic functions of order alpha

Aouf M.

Demonstratio Mathematica

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2007

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Vol. 40, nr 2

317-330

EN

The object of the present paper is to derive various properties and char- acteristics of certain subclasses of p-valently analytic functions of order alpha in the open unit disc by using the techniques involving the Briot-Bouquet differential subordination.

11

Certain subclasses of multivalent prestarlike functions with negative coefficients

Aouf M.

Demonstratio Mathematica

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2007

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Vol. 40, nr 4

799-814

EN

The object of the present paper is to investigate coefficient estimates and closure theorems for functions belonging to the class R[..] of p-valent prestarlike functions with negative coefficients. We also consider integral operators associalted with functions belonging to the class R[..]. Furthermore, distortion theorems involving a generalized fractional integral (derivative) opertaor for functions in this class are proved.

12

On sufficient condition for starlikeness of certain integral of analytic function

Sokół J.

Journal of Mathematics and Applications

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2006

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Vol. 28

127-130

EN

The author aims at finding certain condition on Re f' which is sufficient for the function Φ(z) = ∫(sup z)(sub 0) (sup f(t))(sub t)dt to be starlike function.

13

Radius problems for a class of analytic functions

Ravichandran V., Khan M., Silverman H., Subramanian K.

Demonstratio Mathematica

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2006

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Vol. 39, nr 1

67-74

EN

In this present paper, we investigate certain radius problems for a class of normalized analytic functions in the open unit disk in the complex plane.

14

On some coefficient conditions for complex harmonic mappings with a pole at the infinity

Sibelska A.

Demonstratio Mathematica

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2006

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Vol. 39, nr 2

335-346

EN

In 1984 J. Clunie and T. Sheil-Small initiated studies of complex functions harmonic in the unit disc. In 1987 W. Hergartner and G. Schober considered mappings of this type, defined in the domain U = {z is an element of C : \z\ > 1}. Several mathematicians examine classes of complex harmonic functions with some coefficient conditions, defined in the unit disc (e.g. [2], [5], [10], [1] [9]) or in U (e.g. [8], [7]). We investigate the classes of mappings harmonic in U with coefficient conditions more general than the considered in paper [8].

15

Stability of the Hadamard product of k-uniformly convex and k-starlike functions in certain neighbourhood

Bednarz U.

Demonstratio Mathematica

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2005

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Vol. 38, nr 4

837--845

16

On the boundedness of the singh integral operator

Miclăuş G.

Demonstratio Mathematica

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2005

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Vol. 38, nr 3

591--594

EN

In this paper we determine some conditions so that the Singh integral operator (1) and thier iterative, when it is applied to functions subordinate at starlike functions, are bounded in U.

17

On a problem H. S. Al-Amiri and M. O. Reade

Singh S., Gupta S.

Demonstratio Mathematica

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2005

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Vol. 38, nr 2

303--311

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.

18

Fixed coefficients for certain subclasses of starlike functions with negative coefficients

Aouf M., Al-Dohiman A.

Demonstratio Mathematica

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2005

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Vol. 38, nr 3

551--565

EN

The main object of this paper is to study the class T*n,c(alfa,beta) of analytic functions with negative coefficients and with fixed second coefficients. Among other results of interest, we derive coefficient estimates, closure properties involving convex linear combinations, growth and distortion theorems, and radii of starlikeness and convexity for functions in the class T*n,c(alfa,beta). Many of these results are further extended to hold true for families of functions with finitely many fixed coefficients.

19

Characterization of subclasses of univalent functions

Trojnar-Spelina L.

Demonstratio Mathematica

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2005

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Vol. 38, nr 1

35--41

EN

We investigate the family of functions f(z) = z +(suma od n=2 do nieskończoności) anzn that are analytic in the unit disk with the property that the domain of values f(z) + 1+ei(alpha):2zf", (alpha is an element of (-pi,pi) is the parabolic region (Imw)2 < 2Rew - 1. Integral representation and convolution characterization are found and some coefficients bounds are given.

20

Some application of theGolusinvariation to the starlike functions with respect to m-symmetric points

Stankiewicz Jan, Szpila Anna

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

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2004

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z. 27 [212]

61-68

EN

In this paper we consider the class of starlike functions with respect to m-symmetric points. Using the integral formula for functions from this class and applying the Golusin variation of the first type we obtain a sharp lower bound for If'(z)I.