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- W2078230287 abstract "Let<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M1><mml:mi>F</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>=</mml:mo><mml:mo stretchy=false>|</mml:mo><mml:mi>z</mml:mi><mml:msup><mml:mrow><mml:mo stretchy=false>|</mml:mo></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>g</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo>+</mml:mo><mml:mi>h</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy=false>)</mml:mo><mml:mo> (</mml:mo><mml:mo stretchy=false>|</mml:mo><mml:mi>z</mml:mi><mml:mo stretchy=false>|</mml:mo><mml:mo><</mml:mo><mml:mn>1</mml:mn><mml:mo stretchy=false>)</mml:mo></mml:math>be a biharmonic mapping of the unit disk<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M2><mml:mrow><mml:mi>𝔻</mml:mi></mml:mrow></mml:math>, where<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M3><mml:mrow><mml:mi>g</mml:mi></mml:mrow></mml:math>and<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M4><mml:mrow><mml:mi>h</mml:mi></mml:mrow></mml:math>are harmonic in<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M5><mml:mrow><mml:mi>𝔻</mml:mi></mml:mrow></mml:math>. In this paper, the Landau-type theorems for biharmonic mappings of the form<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M6><mml:mi>L</mml:mi><mml:mo stretchy=false>(</mml:mo><mml:mi>F</mml:mi><mml:mo stretchy=false>)</mml:mo></mml:math>are provided. Here<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M7><mml:mrow><mml:mi>L</mml:mi></mml:mrow></mml:math>represents the linear complex operator<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M8><mml:mi>L</mml:mi><mml:mo>=</mml:mo><mml:mi>(z</mml:mi><mml:mo>∂</mml:mo><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:mi>z)</mml:mi><mml:mo>-</mml:mo><mml:mover><mml:mrow><mml:mi>(z</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover><mml:mo>∂</mml:mo><mml:mo>/</mml:mo><mml:mo>∂</mml:mo><mml:mover><mml:mrow><mml:mi>z)</mml:mi></mml:mrow><mml:mo>¯</mml:mo></mml:mover></mml:math>defined on the class of complex-valued<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML id=M9><mml:mrow><mml:msup><mml:mrow><mml:mi>C</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math>functions in the plane. The results, presented in this paper, improve the related results of earlier authors." @default.
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- W2078230287 date "2014-01-01" @default.
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- W2078230287 title "Landau-Type Theorems for Certain Biharmonic Mappings" @default.
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- W2078230287 doi "https://doi.org/10.1155/2014/925947" @default.
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