SOME RESULTS ASSOCIATED WITH THE ANALYTIC PART OF HARMONIC UNIVALENT FUNCTIONS

Abdul Rahman S. Juma (India), S. R. Kulkarni (India) and R. K. Raina (India)

Received July 19, 2007

References:

[1] Y. Avci and E. Zlotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Sk»odowska Sect. A 44 (1990), 1-7. [2] S. Bhatt and R. K. Raina, A new class of analytic functions involving certain fractional derivative operators, Acta Math. Univ. Comenian 68 (1999), 179-193. [3] J. M. Jahangiri, Harmonic functions starlike in the unit disk, J. Math. Anal. Appl. 235 (1999), 470-477. [4] S. Owa, On the distortion theorems I, Kyungpook Math. J. 18 (1978), 53-59. [5] R. K. Raina and H. M. Srivastava, A certain subclass of analytic functions associated with operators of fractional calculus, Comput. Math. Appl. 32(7) (1996), 13-19. [6] H. M. Srivastava, M. Saigo and S. Owa, A class of distortion theorems involving certain operators of fractional calculus, J. Math. Anal. Appl. 131 (1988), 412-420. [7] H. Silverman, Harmonic univalent function with negative coefficients, J. Math. Anal. Appl. 220 (1998), 283-289.

Keywords and phrases: harmonic functions, analytic and univalent functions, distortion theorems, fractional calculus operators, radii of starlike, close-to-convex and convex functions.