The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

Maisarah Haji Mohd and Maslina Darus

International Journal of Mathematics and Mathematical Sciences, 2011, vol. 2011, 1-8

Abstract:

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form ð ‘“ ( 𠑧 ) = 𠑧 â„Ž ( 𠑧 ) ð ‘” ( 𠑧 ) defined on the open unit disc 𠑈 . The functions are in the class of the generalized Janowski starlike log-harmonic mapping, 𠑆 ∗ l h ( ð ´ , ð µ , ð ›¼ ) , with the functional 𠑧 â„Ž ( 𠑧 ) in the class of the generalized Janowski starlike functions, 𠑆 ∗ ( ð ´ , ð µ , ð ›¼ ) . By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, ð ¶ ð ‘† 𠑇 l h ( ð ´ , ð µ , ð ›¼ ) .

Date: 2011
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:356915

DOI: 10.1155/2011/356915

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