Korean J. Math. Vol. 25 No. 3 (2017) pp.389-403
DOI: https://doi.org/10.11568/kjm.2017.25.3.389

A few results on Janowski functions associated with $k$-symmetric points

Main Article Content

Fuad S Al Sarari
Sridhar Latha
Maslina Darus


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.

Article Details

Supporting Agencies

Universiti Kebangsaan Malaysia


[1] W. Janowski, Some extremal problems for certain families of analytic functions, Ann. Polon. Math. 28 (3), (1973), 297–326. Google Scholar

[2] 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. Google Scholar

[3] 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. Google Scholar

[4] S. Miller, And P. T. Mocanu, Differential Subordinations Theory and Applications Marcel Dekker, New and York-Basel, 2000. Google Scholar

[5] F. Al-Sarari and S.Latha, Conic regions and symmetric points, Int. J. Pure. Appl. Math, 97 (3), (2014), 273–285. Google Scholar

[6] 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. Google Scholar

[7] P. L. Duren, Univalent Functions, Springer-Verlag, 1983. Google Scholar

[8] 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. Google Scholar

[9] R. Singh and M. Tygel, On some univalent functions in the unit disc, Indian. J. Pure. Appl. Math. 12 (1981), 513–520. Google Scholar

[10] S. Ponnusamy, Some applications of differential subordination and convolution techniques to univalent functions theory, Ph. D. thesis, I. I. T. Kanpur, India. (1988). Google Scholar

[11] S. Ruschewyh, Neighborhoods of univalent functions, Proc. Amer. Math. Soc. 81 (1981), 521–527. Google Scholar

[12] K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1), (1959), 72–75. Google Scholar

[13] 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. Google Scholar

[14] A. W. Goodman, Univalent functions and nonanalytic curves, Proc. Amer. Math. Soc. 8 (1957), 598–601. Google Scholar