Volterra type operator on the convex functions

In this paper we study the Volterra type operatör $I_g$ on convex functions. Furthermore, some new properties for convex, starlike and spirallikefunctions of complex order are discussed.

___

  • CHUAQUI, M., DUREN, P. L., OSGOOD, B.: Schwarzian derivatives of convex mapping, Annales Academiae Scientiarum Fennicae Mathematica. V. 39, (2011), 449–460.
  • DUREN, P. L.: Univalent Univalent functions, Springer-Verlag New York, 1983.
  • GRAHAM, I., KOHR, G.: Geometric function theory in one and higher dimensions, Marcel Dekker, Inc New York, 2003.
  • HAYAMI, T., OWA, S.: New properties for starlike and convex functions of complex order, Int. J. Math. Analysis, V. 4 (2007), 39–62.
  • HAYAMI, T., OWA, S., SRIVASTAVA, H, M.: Coefficient inequalities for certain classes of analytic and univalent function, J. Ineq. Pure and Appl. Math. V. 8 (2007), 1–10.
  • NEHARI, Z.: A property of convex conformal maps, J. Analyse Math. 30, (1976), 390–393.
  • LI, S.: Volterra composition operators between weighted Bergman spaces and Bloch-type spaces, J. Korean Math. Soc, 45 no. 1 (2008), 229–248.
  • LI, S., STEVIC, S.: Products of composition and integral type operator from H1 to the Bloch space, Complex Variable Elliptic Functions, 53 no. 5 (2008), 463–474.
  • LI, S., STEVIC, S.: Products of Volterra type operator and composition operator from H1 and Bloch space to the Zygmund space, J. Math. Anal. Appl., 345 no. 1 (2008), 40–52.
  • LI, S., STEVIC, S.: Products of integral-type operators and composition operators between Bloch-type spaces to the Zygmund space, J. Math. Anal. Appl., 349 no. 2 (2009), 596–610.
  • SILVERMANN, H., SILVIA, E, M., TELAGE, D.: Convolution conditions for convexity, starlikeness and spiral-likeness, Math. Z. 162 (1978), 125–130.
  • YONEDA, R.: Pointwise multipliers from BMOA to BMOA Complex Variable, 49(14)(2004), 1045–1061.