A few results on Janowski functions associated with $k$-symmetric points
The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with respect to $k$-symmetric points. We also study certain interesting properties like covering theorem, convolution condition, neighborhood results and argument theorem.
W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math. 28 (3), (1973), 297–326.
M. Haji Mohd and M. Darus, On a class of spiral-like functions with respect to a boundary point related to subordination, Journal of Inequalities and Applications 1, (2013), 274.
O. Kwon and Y. Sim, A certain subclass of Janowski type functions associated with k-symmetic points, Commun. Korean. Math. Soc. 28 (1), (2013), 143–154.
S. Miller, And P. T. Mocanu, Differential Subordinations Theory and Applications Marcel Dekker, New and York-Basel, 2000.
F. Al-Sarari and S.Latha, Conic regions and symmetric points, Int. J. Pure. Appl. Math, 97 (3), (2014), 273–285.
Y. Polatoglu, M. Bolcal, A. Sen and E. Yavuz, A study on the generalization of Janowski functions in the unit disc, Acta Mathematica. Academiae Paedagogicae Nyregyhziensis. 22 (2006), 27–31.
P. L. Duren, Univalent Functions, Springer-Verlag, 1983.
F. Al Sarari and S. Latha, A few results on functions that are Janowski starlike related to (j, k)-symmetric points, Octagon Mathematical Magazine. 21 (2), (2013), 556–563.
R. Singh and M. Tygel, On some univalent functions in the unit disc, Indian. J. Pure. Appl. Math. 12 (1981), 513–520.
S. Ponnusamy, Some applications of differential subordination and convolution techniques to univalent functions theory, Ph. D. thesis, I. I. T. Kanpur, India. (1988).
S. Ruschewyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), 521–527.
K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1), (1959), 72–75.
F. Al-Sarari and S. Latha, A note on Janowski functions with respect to (2j, k)-symmetric conjugate points, IOSR-JRME. (Mar-Apr.2014), 39-47.
A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598–601.
- There are currently no refbacks.
ISSN: 1976-8605 (Print), 2288-1433 (Online)
Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: email@example.com