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ON α-CONVEX FUNCTIONS OF ORDER β OF RUSCHEWEYH TYPE
摘要
In this paper we consider functions f(z) = z^P +α_(p+1) z^(p+1) + ... which are regular in the unit disc E = {z :|z| ＜ 1} and satisfying the condition Re {(1-α)(z^n f)^((n+P))/ [(n+p)(z^(n-1) f)^((n+p-1)] +α(z^(n+1) f)^((n+p+1))/[(n+p+ 1)(z^n f)^((n+p))]} ＞ β. We obtain lower bound γ(α, β, n, p) such that Re {(z^n f)^((n+p))/[(n+p)(z^(n-1) f)^((n+p-1))]} ＞γ(α, β, n, p), where p is positive integer, n is any integer greater than -p, β ＜ 1 and α is real.
延伸閱讀
- Wei, H. (2016). The Study on Convex Functions in a Closed Convex Set [master's thesis, National Taiwan Normal University]. Airiti Library. https://doi.org/10.6345/NTNU202204540
- Guney, H. Ö., & Salagean, G. S. (2007). Further Properties of β-Pascu Convex Functions of Order α. International Journal of Mathematics and Mathematical Sciences, 2007(), 305-311. https://doi.org/10.1155/2007/34017
- MA, W. (1990). ON α-CONVEX FUNCTIONS OF ORDER β WITH M-FOLD SYMMETRY. International Journal of Mathematics and Mathematical Sciences, 1990(), 287-293. https://doi.org/10.1155/S0161171290000424
- AOUF, M. (1988). ON A CLASS OF p-VALENT CLOSE-TO-CONVEX FUNCTIONS OF ORDER β AND TYPE α. International Journal of Mathematics and Mathematical Sciences, 1988(), 259-266. https://doi.org/10.1155/S0161171288000316
- NOOR, K. I. (1992). ON SUBCLASSES OF CLOSE-TO-CONVEX FUNCTIONS OF HIGHER ORDER. International Journal of Mathematics and Mathematical Sciences, 1992(), 279-289. https://doi.org/10.1155/S016117129200036X