Abstract
References
- 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.
Abstract
In this paper we study the Volterra type operatör $I_g$ on convex functions. Furthermore, some new properties for convex, starlike and spirallike
functions of complex order are discussed.
Keywords
Integral operators convex functions of complex order starlike functions of complex order spirallike functions of type $\lambda$ with complex order Schwarzian derivative Schwarzian norm composition operator Volterra type operator
References
- 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.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Research Article |
| Authors | |
| Publication Date | February 1, 2018 |
| Published in Issue | Year 2018 Volume: 47 Issue: 1 |