scholarly journals On Geometric Properties of Normalized Hyper-Bessel Functions

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 316
Author(s):  
Khurshid Ahmad ◽  
Saima Mustafa ◽  
Muhey Din ◽  
Shafiq ur Rehman ◽  
Mohsan Raza ◽  
...  
Keyword(s):  
Hardy Spaces ◽  
Unit Disc ◽  
Bessel Functions ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Geometric Properties

In this paper, the normalized hyper-Bessel functions are studied. Certain sufficient conditions are determined such that the hyper-Bessel functions are close-to-convex, starlike and convex in the open unit disc. We also study the Hardy spaces of hyper-Bessel functions.

scholarly journals A certain class of q-close-to-convex functions of order α

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2295-2305
Author(s):  
Ben Wongsaijai ◽  
Nattakorn Sukantamala
Keyword(s):  
Hypergeometric Function ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Bieberbach Conjecture ◽  
Gaussian Hypergeometric Function ◽  
Geometric Properties

For every 0 < q < 1 and 0 ? ? < 1, we introduce a class of analytic functions f on the open unit disc D with the standard normalization f(0)= 0 = f'(0)-1 and satisfying |1/1-?(z(Dqf)(z)/h(z)-?)- 1/1-q,(z?D), where h?S*q. This class is denoted by Kq(?), so called the class of q-close-to-convex-functions of order ?. In this paper, we study some geometric properties of this class. In addition, we consider the famous Bieberbach conjecture problem on coefficients for the class Kq(?). We also find some sufficient conditions for the function to be in Kq(?) for some particular choices of the functions h. Finally, we provide some applications on q-analogue of Gaussian hypergeometric function.

scholarly journals Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Saibah Siregar ◽  
Maslina Darus
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Subordination Result ◽  
Jack’S Lemma ◽  
Jack's Lemma

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

scholarly journals Univalence criteria for general integral operators involving normalized Dini functions

Filomat ◽  
2020 ◽  
Vol 34 (7) ◽  
pp. 2203-2216
Author(s):  
Muhey Din ◽  
Mohsan Raza ◽  
Erhan Deniz
Keyword(s):  
Unit Disc ◽  
Sufficient Conditions ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disc ◽  
General Integral ◽  
Univalence Criteria

In this paper our aim is to deduce some sufficient conditions for integral operators involving normalized Dini functions to be univalent in the open unit disc. The key tools in our proofs are the generalized versions of the well-known Ahlfor?s and Becker?s univalence criteria and some inequalities for the normalized Dini functions.

scholarly journals Some new harmonic mappings convex in one direction and their convolution

Filomat ◽  
2019 ◽  
Vol 33 (19) ◽  
pp. 6131-6139
Author(s):  
Chinu Singla ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Unit Disc ◽  
Sufficient Conditions ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disc ◽  
Hadamard Products ◽  
New Family ◽  
Convex In One Direction ◽  
A New Technique ◽  
Necessary And Sufficient

In the present article, we construct a new family of locally univalent and sense preserving harmonic mappings by considering a suitable transformation of normalized univalent analytic functions defined in the open unit disc D. We present necessary and sufficient conditions for the functions of this new family to be univalent. Apart from studying properties of this new family, results about the convolutions or Hadamard products of functions from this family with some suitable analytic or harmonic mappings are proved by introducing a new technique which can also be used to simplify the proofs of earlier known results on convolutions of harmonic mappings. The technique presented also enables us to generalize existing such results.

Kadec–Klee properties of vector-valued Hardy spaces

1992 ◽  
Vol 111 (3) ◽  
pp. 535-544 ◽  
Author(s):  
P. N. Dowling ◽  
C. J. Lennard
Keyword(s):  
Banach Space ◽  
Uniform Convergence ◽  
Hardy Spaces ◽  
Unit Disc ◽  
Open Unit ◽  
Uniformly Convex ◽  
Open Unit Disc ◽  
Vector Valued ◽  
Sequence Of Functions ◽  
Compact Subsets

In 1930, S. Warschawski [19] showed that H1(D), where D is the open unit disc in ℂ, has the following property: Let be a sequence of functions in H1(D) converging uniformly on compact subsets of D to a function f∈H1(D) and suppose that ‖fn‖1 = |f‖1 = 1 for all n∈ℕ. Then converges to zero. From a Banach space standpoint, this result says that H1(D) has the Kadec–Klee property with respect to uniform convergence on compact subsets of D. Warschawski's result was proved independently by Newman [16] in 1963 (see also [13] for another proof) and extended to more general domains by Hoffman [12], Goldstein and Swaminathan [8] and Godefroy [7]. A uniform version of Warschawski's result and its subsequent extensions was recently obtained by Besbes, Dilworth, Dowling and Lennard [2] (see also [1]). We mention here that these results for H1 spaces also hold for the Hp-spaces for 1 < p < ∞ because these spaces are uniformly convex.

scholarly journals On the strongly starlikeness of multivalently convex functions of orderα

2001 ◽  
Vol 28 (1) ◽  
pp. 51-55
Author(s):  
Mamoru Nunokawa ◽  
Shigeyoshi Owa ◽  
Akira Ikeda
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc

The object of the present paper is to derive some sufficient conditions for strongly starlikeness of multivalently convex functions of orderαin the open unit disc.

scholarly journals The spectra of Toeplitz operators with unimodular symbols

1998 ◽  
Vol 41 (1) ◽  
pp. 133-139 ◽  
Author(s):  
Takahiko Nakazi
Keyword(s):  
Toeplitz Operator ◽  
Unit Disc ◽  
Toeplitz Operators ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc

The spectrum σ(Tφ) of a Toeplitz operator Tφ on the open unit disc D for a unimodular symbol φ is studied and many sufficient conditions for σ(Tφ)⊆∂D or σ(Tφ) = are given. In particular if φ is a unimodular function in H∞ + C, then σ(Tφ)⊆∂D or σ(Tφ) =

scholarly journals Radial growth and boundedness for Bloch functions

1990 ◽  
Vol 42 (1) ◽  
pp. 33-39 ◽  
Author(s):  
A. Bonilla ◽  
F. Perez Gonzalez
Keyword(s):  
Complex Plane ◽  
Wide Class ◽  
Unit Disc ◽  
Radial Growth ◽  
Bloch Space ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Boundedness Condition ◽  
Significant Extension

Let B be the Bloch space of all those functions f holomorphic in the open unit disc D of the complex plane satisfying . We establish sufficient conditions for the boundedness of functions f belonging to B satisfying a certain uniform radial boundedness condition, and, by introducing a wide class of subsets E of ∂D, which we call negligible sets for boundedness, we show that if f ∈ B and there is a constant K > 0 such that , then f is bounded in D. Hence a significant extension of a theorem of Goolsby is obtained.

An argument of a function in H1/2

2012 ◽  
Vol 55 (2) ◽  
pp. 507-511
Author(s):  
Takahiko Nakazi ◽  
Takanori Yamamoto
Keyword(s):  
Hardy Space ◽  
Simple Proof ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

AbstractLet H1/2 be the Hardy space on the open unit disc. For two non-zero functions f and g in H1/2, we study the relation between f and g when f/g ≥ 0 a.e. on ∂D. Then we generalize a theorem of Neuwirth and Newman and Helson and Sarason with a simple proof.

scholarly journals Harmonic univalent functions defined by post quantum calculus operators

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disc ◽  
Quantum Calculus ◽  
Special Cases ◽  
The Family ◽  
Covering Theorems

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.

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