On Generalized k-Uniformly Close-to-Convex Functions of Janowski Type

Main Article Content

Afis Saliu


This work is concerned with the class of analytic functions that maps open unit disk onto conic domains. Necessary condition, arc length, growth rate of coefficients, radius problems and property of some integral transformation under the class are examined.

Article Details


  1. D.A. Brannan, On Functions of Bounded Boundary Rotation, Proc. Edln. Math. Soc. 2(1968/69), 330-347.
  2. G. Golusin, On distortion theorems and coefficients of univalent functions, Mat. Sb. 19(1946), 183-203 .
  3. A.W. Goodman, On close-to-convex functions of higher order, Ann. Univ. Sci. Budapest, E ¨ot ¨ous Sect. Math., 25(1972), 17-30
  4. A.W. Goodman, Univalent functions, Vols. I& II, Polygonal Publishing House, Washinton, 1983.
  5. W.K. Hyman, On functions with positive real part, J. London Math. Soc. 36(1961), 34-48.
  6. W. Janowski, Some extremal problems for certain families of analytic functions, I, Ann. Polon. Math. 28 (1973), 297-326.
  7. S. Kanas and A. Wisniowska, Conic regions and k-uniform convexity, J. Comput. Appl. Math. 105(1999), 327-336.
  8. S. Kanas and A. Wisniowska, Conic domains and starlike functions, Rev. Roum. Math. Pures Appl. 45(2000), 647-657.
  9. S. Kanas, Coefficient estimates in subclasses of the Caratheodory class related to conical domain, Acta Math. Univ. Comenian, 74(2005), no. 2, 149-161.
  10. W. Kaplan, Close-to-convex Schilcht Functions, Mich. Math. J. 1 (1952), 169-185.
  11. S. Kumar and C. Ramesha, Subordination properties of uniformly convex and uniformly close to convex functions, J. Ramanujan Math. Soc. 9 (1994), no. 2, 203-214.
  12. M. Shahi, A. Muhammad and N.M. Sarfraz, Janoswski type close-to-convex functions associated with conic regions, J. Ineq. Appl. 2017,1(2017), 259.
  13. B.S. Mehrok, A Subclass of Close-to-Convex Functions, Int. J. Math. Anal, 4,(2010), no. 27, 1319-1327.
  14. K.I. Noor and M.A. Noor, Higher Order Close-to-Convex Functions related with Conic Domain, Appl. Math. Inf. Sci. 8(2014), no. 5, 2455.
  15. K.I. Noor, On a generalization of close-to-convexity, Internat. J. Math. Math. Sci. 6(1983), no. 2, 327-334.
  16. K.I. Noor, On subclasses of close-to-convex functions of higher order, Internat. J. Math. Math. Sci. 15(1992), no. 2, 279-290.
  17. K.I. Noor, On a generalization of uniformly convex and related functions, Comput. Math. Appl. 61(2011), 117-125.
  18. K.I. Noor and S.N. Malik, On coefficient inequalities of functions associated with conic domains, Comput. Math. Appl. 62(2011), 2209-2217.
  19. K.I. Noor and M.A. Salim, On some classes of analytic functions, J. Inequal. Pure Appl. Math. 5(2004), no. 4, 98.
  20. F. Ronning, Uniform convex functions and a corresponding class of starlike functions, Proc. Amer. Math. Soc. 118(1993), 189-196.
  21. B. Pinchuk, A variational method for functions of bounded boundary rotation, Trans. Amer. Math. Soc. 138(1969) 107-113.
  22. B. Pinchuk, Functions with bounded boundary rotation, Isr. J. Math. 10 (1971), 716.
  23. E.M. Silvia, Subclasses of close-to-convex functions, Int. J. Math. Math. Sci. 3(1983), 449-458.
  24. K.G. Subramanian, T.V. Sudharsan and H. Silverman , On uniforly close-to-convex functions and uniformly quasiconvex functions, Int.J. Math. Math. Sci.48(2003), 3053-3058.
  25. D.K. Thomas, On starlike and close-to-convex univalent functions, J. Lond. Math. Soc. 42 (1967), 427-435.