Wyniki wyszukiwania - BazTech

1

The order of starlikeness of uniformly convex functions

Wiśniowska-Wajnryb A.

Journal of Applied Analysis

|

2017

|

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.

2

Stability of the integral transformation of k-uniformly convex and k-starlike functions

Bednarz U.

Journal of Mathematics and Applications

|

2007

|

Vol. 29

91-98

EN

For a constant k ϵ [0, ∞) a normalized function f, analytic in the unit disk, is said to be k-uniformly convex if Re (1+z f" (z)/f'(z)) > k|zf"(z)/f'(z)| at any point in the unit disk. The class of k-uniformly convex functions is denoted k-UCV (cf. [8]). The function g is said to be k-starlike if g(z) = zf'(z) and f ϵ k-UCV. For analytic function f, where f(z) = z + a2z² + źźź the integral transformation is defined as follows: [wzór]. Generalized neighbourhood is defined as: [wzór]. In this note a problem of stability of the integral transformation of k-uniformly convex and k-starlike functions for TNδ neighbourhoods is investigated.

3

Stability of the integral convolution of k-uniformly convex and k-starlike functions

Bednarz U., Kanas S.

Journal of Applied Analysis

|

2004

|

Vol. 10, nr 1

105-115

EN

For a constant k ∈ [0, ∞) a normalized function f, analytic in the unit disk, is said to be k-uniformly convex if Re(1 + zf"(z)/f'(z)) > k|zf"(z)/f'(z)| at any point in the unit disk. The class of k-uniformly convex functions is denoted k-UCV (cf. [4]). The function g is said to be k-starlike if g(z) = zf'(z) and f ∈ k-UCV. For analytic functions f, g, where f(z) = z + a2z² + • • • and g(z) = z + b2z² + • • •, the integral convolution is defined as follows: [wzór] In this note a problem of stability of the integral convolution of k-uniformly convex and k-starlike functions is investigated.

4

Generalized neighbourhoods and stability of convolution for the class of k-uniformly convex and k-starlike functions

Bednarz U., Kanas S.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

|

1999

|

z. 23 [175]

29-38

EN

Let k-UCV denote the class of k-uniformly convex functions and let k-ST be the related class of k-starlike functions. For [..] > 0 and nonnegative sequence {tn] we define generalized neighbourhood [...].

5

Differential subordinationfor domains bounded by hyperbolas

Kanas S., Lecko A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

|

1999

|

z. 23 [175]

61-70

EN

Let the function pa,b,s-so with a, b real, nonnegative numbers and s, so is an element of R, be a conform al mapping of the unit disk onto a hyperbolic domain. We establish the conditions udner which the differential subordination of the type p(z) +[...]zp'(z) -< pa,b,s-so(^) yields p -< pa,b,s- so(z) yields p [...] pa,b,s in U. Some applications of obtained results are given.

6

Conic regions k-uniform convexity, II

Kanas S., Wiśniowska A.

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

|

1998

|

z. 22 [170]

65-78

EN

In the previous paper, due to authors, the class of k-uniformly convex functions, (0 < k < oo), has been introduced. Mentioned denoted by kUCV, is a generalization of the class of uniformly convex functions introduced by Goodman, and studied by Ronning, Ma and Minda. This paper is a continuation of investigation of the class k-UCV for that the region of values of 1+ zf'(z)/f'(z), where/ f is an element of k-UCV, is a domain bounded by the conic curves, which kind depends of the parameter k. The estimates of If"(z)I, bounds of coefficients of k-uniformly convex functions, the sharp bounds on |anI, for n= 2,3,4, and the extremal functions which realize equality are given. Some particular examples of functions having the required properties are found.