A CONVOLUTION APPROACH TO CERTAIN SUBCLASSES OF STARLIKE FUNCTIONS

Main Article Content

T . RAM REDDY
O. P. JUNEJA
K. SATHYANARAYANA

Abstract




The class $R_\gamma(A,B)$ for $-1\le B < A\le 1$ and $\gamma> (A- 1)/(1- B)$ consisting of normalised analytic functions in the open unit disc is defined with the help of Convolution technique. It consists of univalent starlike functions for $\gamma\ge 0$. We establish containment property, integral transforms and a sufficient condition for an analytic function to be in $R\gamma(A,B)$. Using the concept of dual spaces we find a convolution condition for a function in this class.




Article Details

How to Cite
REDDY, T. . R., JUNEJA, O. P. ., & SATHYANARAYANA, K. (1992). A CONVOLUTION APPROACH TO CERTAIN SUBCLASSES OF STARLIKE FUNCTIONS. Tamkang Journal of Mathematics, 23(4), 311–320. https://doi.org/10.5556/j.tkjm.23.1992.4554
Section
Papers

References

O. P. Ahuja and H. Silverman, "Function classes related to Ruscheweyh derivatives", J . Austral. Math. Soc., (Series A) 47 (1989), 438-444.

I. S. Jack, "Functions starlike and convex of order alpha", J. Lon. Math. Soc. (2) 3 (1971), 469-474.

W. Janowski, "Some extremal probleins for certain families of analytic functions I", Ann. Polon. Math. 28 (1973), 297-326.

T. Ram Reddy, "A study on certain subclasses of univalent analytic functions'', Ph. D. Thesis, I. T. Kanpur, 1983.

Ram Singh and Sunder Singh, "Integrals of certain univalent functions", Proc. Amer. Math. Soc. 77 (1979), 336-340.

S. Ruscheweyh, "Duality for Hadamard products with applications to extremal problems for functions regular in the unit disc", Trans. Amer. Math. Soc. 210 (1975), 63-74.

S. Ruscheweyh and T . Sheil-Small, "Hadamard product of schlicht functions and Polya Schoenberg Conjecture", Comment. Math. Helve., 48 (1973), 119-135.

K. Sathyanarayana and T. R. Reddy, "An applications of convolution for a subclasses of starlike functions (Communicated)".

T. Sheil-Small, H. Silverman and E. M. Silvia, "Convolution multipliers and starlike functions", J. Analyse. Math., 41 (1982), 181-192.

H. Silverman, E. M. Silvia and D. N. Telage, "Convolution conditions for convesity", starlikeness and spirallikeness. Math. Z., 162 (1978), 125-130.

Similar Articles

1 2 3 4 > >> 

You may also start an advanced similarity search for this article.