On Stability of Convolution of Janowski Functions
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Abstract
In this paper, the classes S*[A,B] and C[A,B] are discussed in terms of dual sets. Using duality, various geometric properties of mentioned class are analyzed. Problem of neighborhood as well as stability of convolution of S*[A,B] and C[A,B] are studied. Some of our results generalize previously known results.
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References
- O. P. Ahuja, Families of analytic functions related to Ruscheweyh derivatives and subordinate to convex functions, Yokohama Math. J., 41(1993), 39-50.
- W. Janowski, Some extremal problems for certain families of analytic functions, I. Ann. Polon. Math., 28(1973), 298-326.
- S. Kanas, Stability of convolution and dual sets for the class of k-uniformly convex and k-starlike functions, Zeszyty Naukowe Politechniki Rzeszowskiej Matematyka, 22(1998), 51-64.
- S. Ponnusamy and V. Singh, Convolution properties of some classes of analytic functions, J. Math. Sci., 89(1998), 1008-1020.
- S. Ruscheweyh, T. Sheil-Small, Hadamard products of Schlicht functions and the Pólya-Schoenberg conjecture, Comment. Math. Helv., 48(1973), 119-135.
- 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, Neighborhoods of univalent functions, Proc. Amer. Math. Soc., 81(1981), 521-527.
- H. Silverman and E. M. Silvia, Subclasses of starlike functions subordinate to convex functions, Canad. J. Math., 37(1985), 48-61.