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1
Content available Eigenvalue asymptotics for potential type operators on lipschitz surfaces of codimension greater than 1
Rozenblum G., Tashchiyan G.
Opuscula Mathematica
|
2018
|
Vol. 38, no. 5
733--758
EN
For potential type integral operators on a Lipschitz submanifold the asymptotic formula for eigenvalues is proved. The reasoning is based upon the study of the rate of operator convergence as smooth surfaces approximate the Lipschitz one.
2
Content available remote Generalized Hilbert Operators on Bergman and Dirichlet Spaces of Analytic Functions
Naik S., Rajbangshi K.
Bulletin of the Polish Academy of Sciences. Mathematics
|
2015
|
Vol. 63, no. 3
227--235
EN
Let f be an analytic function on the unit disk D. We define a generalized Hilbert-type operator Ha, b by Ha, b (f)(z) = [WZÓR], where a and b are non-negative real numbers. In particular, for a=b=β, Ha, b becomes the generalized Hilbert operator Hβ, and β=0 gives the classical Hilbert operator H. In this article, we find conditions on a and b such that Ha, b is bounded on Dirichlet-type spaces Sp, 0 < p < 2, and on Bergman spaces Ap, 2 < p < ∞. Also we find an upper bound for the norm of the operator Ha, b. These generalize some results of E. Diamantopolous (2004) and S. Li (2009).
3
Content available On some classes of meromorphic functions defined by subordination and superordination
Totoi A.
Opuscula Mathematica
|
2011
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Vol. 31, no. 4
651-668
EN
Let p ∈ N* and β,γ ∈ C with β,≠ 0 and let ∑p denote the class of meromorphic functions of the form g(z) = α-p/zp + α0 + α1z + …, z ∈ U, α-p ≠ 0. We consider the integral operator Jp,β,γ : Kp,β,γ: ⊂ ∑p → ∑p defined by [formula]. We introduce some new subclasses of the class ∑p, associated with subordination and superordination, such that, in some particular cases, these new subclasses are the well-known classes of meromorphic starlike functions and we study the properties of these subclasses with respect to the operator Jp,β,γ.
4
Content available remote Univalence criterion for certain integral operators
Hamada H.
Demonstratio Mathematica
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2005
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Vol. 38, nr 1
43--46
EN
Pescar investigated the univalence of certain integral operators. We will show that the results are obtained by the Schwarz lemma. We will also give some generalizations.
5
Content available remote On the boundedness of the singh integral operator
Miclăuş G.
Demonstratio Mathematica
|
2005
|
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.
6
Content available remote Linear invariance and integral operators of univalence functions
Dorff M., Szynal J.
Demonstratio Mathematica
|
2005
|
Vol. 38, nr 1
47--57
EN
In this paper, we study a larger set than (1), namely the set of the minimal invariant family which contains (1), where / belongs to the linear invariant family, and thereby we obtain information about the univalence of (1). In particular, we determine the order of this minimal invariant family in the cases of univalent and convex univalent functions in D. As a result, we find the radius of close-to-convexity and the lower bound for the radius of univalence for the minimal invariant family in the case of convex univalent functions. This allows us to determine the exact region for (a, (3) where the corresponding minimal invariant family is univalent and close-to-convex. These results are sharp and generalize those which were obtained in [11].
7
The univalence of integral operator
Blezu Dorin, Raducanu Dorina
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2002
|
z. 26 [199]
45-50
EN
The aim of this paper is to obtain some univalence criteria in connection with integral operators due to E.Cazacu, S.Moldovan and N.N.Pascu. Thus we use another univalence criterion which is based of the well-known Becker's criterion but it does't depend of \z\. For this reason these are easily used for practical applications.
8
Solution of Fredholm integral of first kind Singular Kernel
El-Bary A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2000
|
z. 24 [181]
27-35
EN
This paper is devoted to give and discuss the method of solving the Fredholm integral equation of the first kind with singular kernel by using the Fourier method.
9
On uniformly [alpha]-close to-convex functions
Durai M., Prabhakaran D.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2000
|
z. 24 [181]
5-14
EN
The transform under Ruscheweyh integral operator of the newly introduced class of uniformly a-close to-convex functions is studied.
10
On the univalence for integral operators
Blezu D., Raducanu D.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2000
|
z. 24 [181]
15-20
EN
The aim of this paper is to obtain some univalence criteria in connection with integral operators due to E. Cazacu, S. Moldovan and N.N. Pascu. In this sens we use an other univalence criterion which is based on the well-known Decker's criterion but is does't depend on \z\. For this reason these are easy used for practical applications.
11
On the starlikeness of certain integral operators
Patel J., Mohanty A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
|
2000
|
z. 24 [181]
79-85
EN
Let A (p) denote the class of functions f (z) =zp+[summation]infinity/k=p+1akzk analytic in the unit disc E. In this paper, we obtain a condition for starlikeness of the integral operator [...].
12
Content available remote Generalized sampling operators in modular spaces
Mantellini I.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
1998
|
[Z] 38
77-92
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