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Subclasses of k-uniformly convex and k-starlike functions defined by S[문자]l[문자]gean operator

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The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc U, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

Abstract

The main object of this paper is to introduce and investigate new subclasses of normalized analytic functions in the open unit disc U, which generalize the familiar class of k-starlike functions. The various properties and characteristics for functions belonging to these classes derived here include (for example) coefficient inequalities, distortion theorems involving fractional calculus, extreme points, integral operators and integral means inequalities.

참고문헌 (12)

  1. P. L. Duren, "Univalent Functions" (1983), Springer-Verlag
  2. A. W. Goodman, "On uniformly convex functions", Ann. Polon. Math, 56(1), pp.87~92 (1991)
  3. A. W. Goodman, "On uniformly starlike functions", J. Math. Anal. Appl, (2), pp.364~370 (1991)
  4. S. Kanas, "Conic regions and k-uniform convexity", J. Comput. Appl. Math, 105(1), pp.327~336 (1999)
  5. S. Kanas, "Conic domains and starlike functions", Rev. Roumaine Math. Pures Appl, 45(4), pp.647~657 (2000)
  6. J. E. Littlew, "On inequalities in the theory of functions", Proc. London Math. Soc, 23(2), pp.481~519 (1925)
  7. W. Ma, "Uniformly convex functions", Ann. Polon. Math, 57(2), pp.165~175 (1992)
  8. S. Owa, "On the distortion theorems", I, Kyungpook Math. J, 18(1), pp.53~59 (1978)
  9. F. Rnning, "Uniformly convex functions and a corresponding class of starlike functions", Proc. Amer. Math. Soc, 118(1), pp.189~196 (1993)
  10. G. S. Salagean, "Subclasses of univalent functions, Complex analysis-fifth Romanian-Finnish seminar, Part 1 (Bucharest, 1981)", Lecture Notes in Math, 1013, pp.362~372 (1983), Springer
  11. G. S. Salagean, "On some classes of univalent functions, Seminar of geometric function theory", Univ. "Babes-Bolyai", Cluj-Napoca, 142~158 (1983)
  12. H. M. Srivastava, "Univalent Functions, Fractional Calculus, and Their Applications" (1989), John Wiley & Sons, Inc

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