Approximation of Harmonic Functions Classes With Singularities on Quasiconformal Curves

Jafarov, Sadulla Z.

doi:10.11650/twjm/1500602439

Cited by 2 publications

(2 citation statements)

References 5 publications

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“…In this study the approximation problems of the functions by Faber-Laurent rational functions in the weighted generalized grand Smirnov classes E p),θ (G, ω), θ > 0, defined in the doubly connected domains with the regular boundaries are studied. Similar problems in the different spaces were investigated by several authors (see for example, [1][2][3][4][5][14][15][16][17][18][19][20][21][22][23]25,[27][28][29][30][31][32]38,39]).…”

Section: Introductionmentioning

confidence: 93%

On approximation of functions by rational functions in weighted generalized grand Smirnov classes

Jafarov

2022

Arab. J. Math.

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Let G be a doubly connected domain in the complex plane $$\mathbb {C}$$ C , bounded by Ahlfors 1-regular curves. In this study the approximation of the functions by Faber–Laurent rational functions in the $$\omega $$ ω -weighted generalized grand Smirnov classes $$\mathcal {E}^{p),\theta }(G,\omega )$$ E p ) , θ ( G , ω ) in the term of the rth$$,~r=1,2\ldots ,$$ , r = 1 , 2 … , mean modulus of smoothness are investigated.

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Section: Introductionmentioning

confidence: 93%

On approximation of functions by rational functions in weighted generalized grand Smirnov classes

Jafarov

2022

Arab. J. Math.

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“…Some direct theorems about the approximation of the functions by the rational functions in different spaces have been investigated by several authors (see, for example, [1,5,8,[10][11][12][14][15][16][17][18]21]). All these results were proved under different restrictive conditions on .…”

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confidence: 99%

Approximation of Functions by Rational Functions on Closed Curves of the Complex Plane

Jafarov

2011

Arab J Sci Eng

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Let be a quasi-smooth curve in the complex plane C. In this study, a direct theorem of approximation theory in certain subclasses of the functions which have continuous derivatives through order r on a closed curve is proved. Mathematics Subject Classification Definitions, Some Auxiliary Results and Main ResultLet be an arbitrary restricted Jordan curve with two-component complements = C = 1 ∪ 2 , (0 ∈ 1 , ∞ ∈ 2 ). Let us consider the functions w = φ i (z), (i = 1, 2), that conformally and univalently map, respectively, i onto i , 1 = {w : |w| < 1}, 2 = {w : |w| > 1} , with norm φ 1 (0) =0, φ 1 (0) > 0, φ 2 (∞) = ∞, lim z→∞ 1 z φ 2 (z) > 0. Let us extend each φ i (z), (i = 1, 2) continuously up to the bound = ∂ 1 = ∂ 2 (generally speaking φ 1 (z) = φ 2 (z) for z ∈ ). We preserve the notation φ i , (i = 1, 2) for the extension. Let z = i (w) be the inverse mapping of w = φ i (z), (i = 1, 2) . LetFor arbitrary natural number n we set1+ (−1) i n (z) := inf ζ 1+ (−1) i n |ζ − z| , ρ1 n (z) := min ρ 1+ (−1) i n (z) , i = 1, 2

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Approximation of Harmonic Functions Classes With Singularities on Quasiconformal Curves

Cited by 2 publications

References 5 publications

On approximation of functions by rational functions in weighted generalized grand Smirnov classes

On approximation of functions by rational functions in weighted generalized grand Smirnov classes

Approximation of Functions by Rational Functions on Closed Curves of the Complex Plane

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