Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings | Zendy

S-H Chen | Zendy; Saminathan Ponnusamy | Zendy; X. Wang | Zendy

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Some Properties and Regions of Variability of Affine Harmonic Mappings and Affine Biharmonic Mappings

Author(s) -

S-H Chen,

Saminathan Ponnusamy,

X. Wang

Publication year - 2009

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2009/834215

Subject(s) - mathematics , biharmonic equation , affine transformation , convexity , pure mathematics , lemma (botany) , social connectedness , subordination (linguistics) , mathematical proof , harmonic , mathematical analysis , geometry , psychology , ecology , linguistics , philosophy , physics , poaceae , quantum mechanics , financial economics , economics , psychotherapist , biology , boundary value problem

We first obtain the relations of local univalency, convexity, and linear connectedness between analytic functions and their corresponding affine harmonic mappings. In addition, the paper deals with the regions of variability of values of affine harmonic and biharmonic mappings. The regions (their boundaries) are determined explicitly and the proofs rely on Schwarz lemma or subordination

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