On Janowski harmonic functions

2015 ◽  
Vol 21 (2) ◽  
Author(s):  
Jacek Dziok
Keyword(s):  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Janowski Functions ◽  
Distortion Theorems ◽  
Necessary And Sufficient

AbstractIn 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.

scholarly journals Classes of harmonic functions defined by convolution

2019 ◽  
Vol 26 (2) ◽  
pp. 399-416
Author(s):  
Jacek Dziok
Keyword(s):  
Harmonic Functions ◽  
Sufficient Conditions ◽  
Extreme Points ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Necessary And Sufficient

Abstract The object of the present paper is to investigate classes of harmonic functions defined by convolution. Some necessary and sufficient conditions, topological properties, radii of convexity and starlikeness, as well as extreme points for the classes are considered.

SOME TOPOLOGICAL RESULTS ON LEVEL SETS AND MULTIFRACTAL SETS

Fractals ◽  
2019 ◽  
Vol 28 (01) ◽  
pp. 2050009
Author(s):  
CHUNTAI LIU
Keyword(s):  
Level Sets ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Symbolic Space ◽  
Necessary And Sufficient

In this paper, we study topological properties of some level sets and some multifractal sets induced by Rademacher’s series and Takagi’s series, respectively. By using symbolic space, we obtain necessary and sufficient conditions for them to be residual.

scholarly journals On the generalized Riesz B-difference sequence spaces

Filomat ◽  
2010 ◽  
Vol 24 (4) ◽  
pp. 35-52 ◽  
Author(s):  
Metin Başarir
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Sequence Spaces ◽  
Matrix Transformations ◽  
Difference Sequence ◽  
Topological Properties ◽  
Linear Spaces ◽  
The Matrix ◽  
Necessary And Sufficient ◽  
Difference Sequence Spaces

In this paper, we define the new generalized Riesz B-difference sequence spaces rq? (p, B), rqc (p, B), rq0 (p, B) and rq (p, B) which consist of the sequences whose Rq B-transforms are in the linear spaces l?(p), c (p), c0(p) and l(p), respectively, introduced by I.J. Maddox[8],[9]. We give some topological properties and compute the ?-, ?- and ?-duals of these spaces. Also we determine the necessary and sufficient conditions on the matrix transformations from these spaces into l? and c.

scholarly journals Fourier coefficients and growth of harmonic functions

1987 ◽  
Vol 10 (3) ◽  
pp. 443-452 ◽  
Author(s):  
A. fryant ◽  
H. Shankar
Keyword(s):  
Harmonic Functions ◽  
Fourier Coefficients ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Several Variables ◽  
Order And Type ◽  
Necessary And Sufficient

We consider Harmonic Functions,Hof several variables. We obtain necessary and sufficient conditions on its Fourier coefficients so thatHis an entire harmonic (that is, has no finite singularities) function; the radius of harmonicity in terms of its Fourier coefficients in caseHis not entire. Further, we obtain, in terms of its Fourier coefficients, the Order and Type growth measures, both in caseHis entire or non-entire.

Topological Properties of a Class of Higher-dimensional Self-affine Tiles

2019 ◽  
Vol 62 (4) ◽  
pp. 727-740
Author(s):  
Guotai Deng ◽  
Chuntai Liu ◽  
Sze-Man Ngai
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Higher Dimensional ◽  
Necessary And Sufficient

AbstractWe construct a family of self-affine tiles in $\mathbb{R}^{d}$ ($d\geqslant 2$) with noncollinear digit sets, which naturally generalizes a class studied originally by Q.-R. Deng and K.-S. Lau in $\mathbb{R}^{2}$, and its extension to $\mathbb{R}^{3}$ by the authors. We obtain necessary and sufficient conditions for the tiles to be connected and for their interiors to be contractible.

scholarly journals Lattice separation, coseparation and regular measures

1996 ◽  
Vol 19 (4) ◽  
pp. 773-779
Author(s):  
Maurice C. Figueres
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Finitely Additive Measures ◽  
Necessary And Sufficient ◽  
Additive Measures

LetXbe an arbitrary non-empty set, and letℒ,ℒ1,ℒ2be lattices of subsets ofXcontainingϕandX.𝒜(ℒ)designates the algebra generated byℒandM(ℒ), these finite, non-trivial, non-negative finitely additive measures on𝒜(ℒ).I(ℒ)denotes those elements ofM(ℒ)which assume only the values zero and one. In terms of aμ∈M(ℒ)orI(ℒ), various outer measures are introduced. Their properties are investigated. The interplay of measurability, smoothness ofμ, regularity ofμand lattice topological properties on these outer measures is also investigated.Finally, applications of these outer measures to separation type properties between pairs of latticesℒ1,ℒ2whereℒ1⊂ℒ2are developed. In terms of measures fromI(ℒ), necessary and sufficient conditions are established forℒ1to semi-separateℒ2, forℒ1to separateℒ2, and finally forℒ1to coseparateℒ2.

scholarly journals Convex functions and the rolling circle criterion

1995 ◽  
Vol 18 (4) ◽  
pp. 799-811
Author(s):  
V. Srinivas ◽  
O. P. Juneja ◽  
G. P. Kapoor
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Rolling Circle ◽  
Circle Criterion ◽  
Rotation Theorem ◽  
Distortion Theorems ◽  
Necessary And Sufficient ◽  
Growth And Distortion Theorems

Given0≤R1≤R2≤∞,CVG(R1,R2)denotes the class of normalized convex functionsfin the unit discU, for which∂f(U)satisfies a Blaschke Rolling Circles Criterion with radiiR1andR2. Necessary and sufficient conditions forR1=R2, growth and distortion theorems forCVG(R1,R2)and rotation theorem for the class of convex functions of bounded type, are found.

SIMPLICITY OF CROSSED PRODUCTS BY TWISTED PARTIAL ACTIONS

2019 ◽  
Vol 108 (2) ◽  
pp. 202-225
Author(s):  
ALEXANDRE BARAVIERA ◽  
WAGNER CORTES ◽  
MARLON SOARES
Keyword(s):  
Hausdorff Space ◽  
Associative Ring ◽  
Sufficient Conditions ◽  
Continuous Functions ◽  
Necessary And Sufficient Conditions ◽  
Crossed Products ◽  
Topological Properties ◽  
Partial Action ◽  
Necessary And Sufficient ◽  
Skew Group Ring

In this article, we consider a twisted partial action $\unicode[STIX]{x1D6FC}$ of a group $G$ on an associative ring $R$ and its associated partial crossed product $R\ast _{\unicode[STIX]{x1D6FC}}^{w}G$. We provide necessary and sufficient conditions for the commutativity of $R\ast _{\unicode[STIX]{x1D6FC}}^{w}G$ when the twisted partial action $\unicode[STIX]{x1D6FC}$ is unital. Moreover, we study necessary and sufficient conditions for the simplicity of $R\ast _{\unicode[STIX]{x1D6FC}}^{w}G$ in the following cases: (i) $G$ is abelian; (ii) $R$ is maximal commutative in $R\ast _{\unicode[STIX]{x1D6FC}}^{w}G$; (iii) $C_{R\ast _{\unicode[STIX]{x1D6FC}}^{w}G}(Z(R))$ is simple; (iv) $G$ is hypercentral. When $R=C_{0}(X)$ is the algebra of continuous functions defined on a locally compact and Hausdorff space $X$, with complex values that vanish at infinity, and $C_{0}(X)\ast _{\unicode[STIX]{x1D6FC}}G$ is the associated partial skew group ring of a partial action $\unicode[STIX]{x1D6FC}$ of a topological group $G$ on $C_{0}(X)$, we study the simplicity of $C_{0}(X)\ast _{\unicode[STIX]{x1D6FC}}G$ by using topological properties of $X$ and the results about the simplicity of $R\ast _{\unicode[STIX]{x1D6FC}}^{w}G$.

scholarly journals On topological properties of the Hausdorff fuzzy metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1167-1173
Author(s):  
Changqing Li ◽  
Kedian Li
Keyword(s):  
Metric Spaces ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Topological Properties ◽  
Fuzzy Metric Spaces ◽  
Fuzzy Metric ◽  
Necessary And Sufficient

In the paper, necessary and sufficient conditions for two Hausdorff fuzzy metric spaces to be homeomorphic are studied. Also, several properties of the Hausdorff fuzzy metric spaces, as F-boundedness, separability and connectedness are explored.

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