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

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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.

Abstract

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.

참고문헌 (14)

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  2. M. Haji Mohd, "On a class of spiral-like functions with respect to a boundary point related to subordination", Journal of Inequalities and Applications, 1, pp.274~ (2013)
  3. 권오상, "A certain subclass of Janowski type functions associated with k-symmetric points", 대한수학회논문집, 28(1), pp.143~154 (2013), 대한수학회
  4. S. Miller, "Differential Subordinations Theory and Applica-tions" (2000), Marcel Dekker
  5. F. Al-Sarari, "Conic regions and symmetric points", Int. J. Pure. Appl. Math, 97(3), pp.273~285 (2014)
  6. Y. Polatoglu, "A study on the generalization of Janowski functions in the unit disc, Acta Mathematica", Academiae Paedagogi-cae Nyregyhziensis, 22, pp.27~31 (2006)
  7. P. L. Duren, "Univalent Functions" (1983), Springer-Verlag
  8. F. Al Sarari, "A few results on functions that are Janowski star-like related to (j; k)-symmetric points", Octagon Mathematical Magazine, 21(2), pp.556~563 (2013)
  9. R. Singh, "On some univalent functions in the unit disc", Indian. J. Pure. Appl. Math, 12, pp.513~520 (1981)
  10. S. Ponnusamy, "Some applications of di erential subordination and convolution techniques to univalent functions theory", Ph. D., pp.1988
  11. S. Ruschewyh, "Neighborhoods of univalent functions", Proc. Amer. Math. Soc, 81, pp.521~527 (1981)
  12. K. Sakaguchi, "On a certain univalent mapping", J. Math. Soc. Japan, 11(1), pp.72~75 (1959)
  13. F. Al-Sarari, "A note on Janowski functions with respect to (2j; k)-symmetric conjugate points", IOSR-JRME, pp.39~47 (2014)
  14. A. W. Goodman, "Univalent functions and nonanalytic curves", Proc. Amer. Math. Soc, 8, pp.598~601 (1957)

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