A note on the functions defined by Ruscheweyn
S. Owa, C. Y. Shen (1988)
Matematički Vesnik
Similarity:
S. Owa, C. Y. Shen (1988)
Matematički Vesnik
Similarity:
H. E. Darwish, A. Y. Lashin, S. M. Sowileh (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
In the present work, we introduce the subclass , of starlike functions with respect to -symmetric points of complex order () in the open unit disc . Some interesting subordination criteria, inclusion relations and the integral representation for functions belonging to this class are provided. The results obtained generalize some known results, and some other new results are obtained.
Saminathan Ponnusamy, Allu Vasudevarao (2010)
Annales Polonici Mathematici
Similarity:
For γ ∈ ℂ such that |γ| < π/2 and 0 ≤ β < 1, let denote the class of all analytic functions P in the unit disk with P(0) = 1 and in . For any fixed z₀ ∈ and λ ∈ ̅, we shall determine the region of variability for when P ranges over the class As a consequence, we present the region of variability for some subclasses of univalent functions. We also graphically illustrate the region of variability for several sets of parameters.
Jacek Dziok (2013)
Annales Polonici Mathematici
Similarity:
We consider functions of the type , where are real numbers and are -strongly close-to-starlike functions of order . We look for conditions on the center and radius of the disk (a,r) = z:|z-a| < r, |a| < r ≤ 1 - |a|, ensuring that F((a,r)) is a domain starlike with respect to the origin.
M. Obradović (1984)
Matematički Vesnik
Similarity:
A. Y. Lashin (2017)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
Let be the class of analytic functions in the unit disc of the complex plane with the normalization . We introduce a subclass of , which unifies the classes of bounded starlike and convex functions of complex order. Making use of Salagean operator, a more general class () related to is also considered under the same conditions. Among other things, we find convolution conditions for a function to belong to the class . Several properties of the class are investigated. ...
Adam Lecko (2002)
Annales Polonici Mathematici
Similarity:
The purpose of this paper is to study the class of univalent analytic functions defined in the right halfplane ℍ and starlike w.r.t. the boundary point at infinity. An analytic characterization of functions in is presented.
Pavel Trojovský (2000)
Mathematica Slovaca
Similarity:
Liulan Li, Saminathan Ponnusamy (2016)
Czechoslovak Mathematical Journal
Similarity:
We consider the class of sense-preserving harmonic functions defined in the unit disk and normalized so that and , where and are analytic in the unit disk. In the first part of the article we present two classes and of functions from and show that if and , then the harmonic convolution is a univalent and close-to-convex harmonic function in the unit disk provided certain conditions for parameters and are satisfied. In the second part we study the harmonic sections...
Lucjan Siewierski
Similarity:
CONTENTSIntroduction...............................................................................................................................................................................5Definitions and notation.........................................................................................................................................................7The main result........................................................................................................................................................................91....
Nicoleta Ularu, Nicoleta Breaz (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
The purpose of this paper is to study some properties related to convexity order and coefficients estimation for a general integral operator. We find the convexity order for this operator, using the analytic functions from the class of starlike functions of order and from the class and also we estimate the first two coefficients for functions obtained by this operator applied on the class .
Mamoru Nunokawa, Emel Yavuz Duman, Shigeyoshi Owa (2013)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
Let denote the class of analytic functions of the form in the open unit disc . Applying the result by S. S. Miller and P. T. Mocanu (J. Math. Anal. Appl. 65 (1978), 289-305), some interesting properties for concerned with Caratheodory functions are discussed. Further, some corollaries of the results concerned with the result due to M. Obradovic and S. Owa (Math. Nachr. 140 (1989), 97-102) are shown.
Daniel Azagra, Mar Jiménez-Sevilla (2002)
Bulletin de la Société Mathématique de France
Similarity:
We study the size of the sets of gradients of bump functions on the Hilbert space , and the related question as to how small the set of tangent hyperplanes to a smooth bounded starlike body in can be. We find that those sets can be quite small. On the one hand, the usual norm of the Hilbert space can be uniformly approximated by smooth Lipschitz functions so that the cones generated by the ranges of its derivatives have empty interior. This implies that there are smooth...
Michael Larsen, Alexander Lubotzky (2008)
Journal of the European Mathematical Society
Similarity:
Let be a group and the number of its -dimensional irreducible complex representations. We define and study the associated representation zeta function . When is an arithmetic group satisfying the congruence subgroup property then has an “Euler factorization”. The “factor at infinity” is sometimes called the “Witten zeta function” counting the rational representations of an algebraic group. For these we determine precisely the abscissa of convergence. The local factor at a finite...
B. A. Frasin (2012)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
Similarity:
In this paper, we obtain new sufficient conditions for the operators and to be univalent in the open unit disc , where the functions belong to the classes and . The order of convexity for the operators and is also determined. Furthermore, and for , we obtain sufficient conditions for the operators and to be in the class . Several corollaries and consequences of the main results are also considered.
M. Anbudurai, R. Parvatham, S. Ponnusamy, V. Singh (2004)
Annales Polonici Mathematici
Similarity:
Let A denote the space of all analytic functions in the unit disc Δ with the normalization f(0) = f’(0) − 1 = 0. For β < 1, let . For λ > 0, suppose that denotes any one of the following classes of functions: , , . The main purpose of this paper is to find conditions on λ and γ so that each f ∈ is in or , γ ∈ [0,1/2]. Here and respectively denote the class of all starlike functions of order γ and the class of all convex functions of order γ. As a consequence, we obtain...
Jun-ichi Tanaka (2008)
Studia Mathematica
Similarity:
The Riemann zeta-function ζ(s) extends to an outer function in ergodic Hardy spaces on , the infinite-dimensional torus indexed by primes p. This enables us to investigate collectively certain properties of Dirichlet series of the form for in . Among other things, using the Haar measure on for measuring the asymptotic behavior of ζ(s) in the critical strip, we shall prove, in a weak sense, the mean-value theorem for ζ(s), equivalent to the Lindelöf hypothesis.