In this paper, we introduce two new subclasses of p-valent spirallike functions of order α : We prove necessary and suffcient conditions for these newly defined classes and also point out some known consequences of our results.
Citation: Nazar Khan, Qazi Zahoor Ahmad, Tooba Khalid, Bilal Khan. Results on spirallike p-valent functions[J]. AIMS Mathematics, 2018, 3(1): 12-20. doi: 10.3934/Math.2018.1.12
In this paper, we introduce two new subclasses of p-valent spirallike functions of order α : We prove necessary and suffcient conditions for these newly defined classes and also point out some known consequences of our results.
| [1] | M. Arif, J. Dziok, M. Raza, et al. On products of multivalent close-to-star functions, J. Ineq. appl., 2015 (2015), 1-14. |
| [2] | N. Khan, B. Khan, Q. Z. Ahmad, et al. Some Convolution properties of multivalent analytic functions, AIMS Math., 2 (2017), 260-268. |
| [3] | R. J. Libera, Univalent spiral functions, Cand. J. Math., 19 (1967), 725-733. |
| [4] | S. S. Miller and P. T. Mocanu, Second order differential inequalities in the complex Plane, J. Math. Anal. Appl., 65 (1978), 289-305. |
| [5] | K. I. Noor, N. Khan and M. A. Noor, On generalized spiral-like analytic functions, Filomat, 28 (2014), 1493-1503. |
| [6] | K. I. Noor and N. Khan, Some convolution properties of a subclass of p-valent functions, Maejo Int. J. Sci. Technol., 9 (2015), 181-192. |
| [7] | K. I. Noor, N. Khan and Q. Z. Ahmad, Coeffcient bounds for a subclass of multivalent functions of reciprocal order, AIMS Math., 2 (2017), 322-335. |
| [8] | K. I. Noor, Q. Z. Ahmad and N. Khan, On a subclasses of meromorphic function define by fractional derivative opretor, Italian J. Pure Appl. Math., 38 (2017), 127-136. |
| [9] | M. Nunokawa, J. Sokoł, On the multivalency of certain analytic functions, J. Ineq. appl., 2014 (2014), 1-9. |
| [10] | M. Nunokawa, S. Hussain, N. Khan, et al. A subclass of analytic functions related with conic domain, J. Clas. Anal., 9 (2016), 137-149. |
| [11] | M. Obradovic and S. Owa, On some results for spiral functions of order α , Internat. J. Math. Math. Sci., 9 (1986), 439-446. |
| [12] | S. Owa, K. Ochiai and H. M.Srivastava, Some coeffcients inequalities and distortion bounds associated with certain new subclasses of analytic functions, Math. Ineq. Appl., 9 (2006), 125-135. |
| [13] | S. Owa and F. S. M. Kamali, On some results for subclass of β -spirallike functions of order α , Tamsui Oxford J. Inf. Math. Sci., 28 (2012), 79-93. |
| [14] | Y. Polatoglu and A. Sen, Some results on subclasses of Janowski λ -spirallike functions of complex order, Gen. Math., 15 (2007), 88-97. |
| [15] | L. Špaček, Příspĕvek k teorii funkcí prostých, Časopis pro pĕstováni matematiky a fysiky, 62 (1933), 12-19. |
Nazar Khan, Qazi Zahoor Ahmad, Tooba Khalid, Bilal Khan. Results on spirallike p-valent functions[J]. AIMS Mathematics, 2018, 3(1): 12-20. doi: 10.3934/Math.2018.1.12
DownLoad: