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  Far East Journal of Mathematical Sciences (FJMS)  
 ISSN: 0972-0871
 
 
 

     Far East Journal of Mathematical Sciences (FJMS)
    Volume 28, Issue 1, Pages 197 - 213 (January 2008)


SOME PROPERTIES OF HARMONIC UNIVALENT FUNCTIONS IN TERMS OF RUSCHEWEYH DERIVATIVES

Waggas Galib Atshan (India) and S. R. Kulkarni (India)

Received June 16, 2007; Revised August 11, 2007

References:



[1] S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc. 135 (1969), 429-446.

[2] J. Clunie and T. Sheil-Small, Harmonic univalent functions, Ann. Acad. Aci. Fenn. Ser. A. I. Math. 9 (1984), 3-25.

[3] A. W. Goodman, On uniformly convex functions, Annal. Polonici Math. 56 (1991), 86-92.

[4] J. M. Jahangiri, Coefficient bounds and univalence criteria for harmonic functions with negative coefficients, Ann. Univ. Marie-Curie-Sklodowska Sect. A 52 (1988), 57-66.

[5] J. M. Jahangiri, Harmonic functions starlike in the unit disc, J. Math. Anal. Appl. 235 (1999), 470-477.

[6] J. M. Jahangiri and H. Silverman, Harmonic univalent functions with varying arguments, Int. J. Appl. Math. 8(3) (2002), 267-275.

[7] J. M. Jahangiri and H. Silverman, Harmonic close-to-convex mappings, J. Appl. Math. Stoch. Anal. 15(1) (2002), 23-28.

[8] T. Rosy, B. A. Stephen, K. G. Subramanian and J. M. Jahangiri, Goodman-Rønning-type harmonic univalent functions, Kyungpook Math. J. 41 (2001), 45-54.

[9] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109-116.

Keywords and phrases: harmonic functions, Ruscheweyh derivative, extreme points, convex combination, convolution and integral operator.

 


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