TY  - JOUR
T1  - q-Meromorphic closed-to-convex functions related with Janowski function
AU  - Sakar, F. Müge
AU  - Shah, Syed Ghoos Ali
AU  - Hussain, Saqib
AU  - Rasheed, Akhter
AU  - Naeem, Muhammad
PY  - 2022
DA  - March
Y2  - 2021
DO  - 10.31801/cfsuasmas.883970
JF  - Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics
JO  - Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.
PB  - Ankara University
WT  - DergiPark
SN  - 1303-5991
SP  - 25
EP  - 38
VL  - 71
IS  - 1
LA  - en
AB  - In the present paper, we introduce and explore certain new classes of meromorphic functions related with closed-to-convexity and q-calculus. Such results ascoefficient estimates, grow the property and partial sums are derived. It is important to mentioned that our results are generalization of number of existingresults in literature.
KW  - Meromorphic starlike function
KW  - Janowski functions
KW  - q-derivative
CR  - Aouf, M. K., Silverman, H., Partial sums of certain meromorphic p-valent functions, J. Inequal. Pure Appl. Math., 7(4), Article 119, (2006).
CR  - Aral, A., Gupta, V., Agarwal, R. P., Applications of q-Calculus in Operator Theory, Springer, New York, USA, 2013.
CR  - Cho, N. E., Owa, S., Sufficient conditions for meromorphic starlikeness and close to-convexity of order α, Int. J. Math. Sci., 26(5) (2001), 317-319. DOI:10.1155/S0161171201004550
CR  - Clunie, J., On meromorphic schlicht functions, J. London Math. Soc., 34 (1959), 215-216.
CR  - Darus, M., Hussain, S., Raza, M., Sokol, J., On a subclass of starlike functions, Results in Mathematics, 73 (2018), 1-12.
CR  - Gasper, G., Rahman, M., Basic Hypergeometric Series, Cambridge University Press Cambridge, 1990.
CR  - Hussain, S., Srivastava, H. M., Raziq, A., Raza, M., The Fekete-Szego functional for subclass of analytic functions associated with quasi-subordination, Carpathian J. Math., 34 (2018), 103-113.
CR  - Ismail, M. E. H., Merkes, E., Styer, D., A generalization of starlike functions, Complex Var. Theory Appl., 14 (1990), 77-84.
CR  - Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193–203.
CR  - Jackson, F. H., q-difference equations, Am. J. Math., 32 (1910), 305–314.
CR  - Janowski, W., Some extrenal problems for certain families of analytic functions, Ann. Pol. Math., 28 (1973), 297–326.
CR  - Khan, B., Liu, Z. G., Srivastava,H. M., Khan, N., Darus, M., Tahir, M., A study of some families of multivalent q-starlike functions involving higher-order q-derivatives, Mathematics, 8 (2020), Article ID 1470, 1-12. DOI:10.3390/math8091470
CR  - Khan, N., Shafiq, M., Darus, M., Khan, B., Ahmad, Q. Z., it Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with Lemniscate of Bernoulli, J. Math. Inequal., 1 (2020), 51–63. DOI:10.7153/jmi-2020-14-05
CR  - Miller, J. E., Convex meromrphic mapping and related functions, Proc. Amer. Math. Soc., 25 (1970), 220-228.
CR  - Miller, S. S., Mocanu, P. T., Differential subordination and univalent functions, Mich. Math. J., 28 (1918), 157–171.
CR  - Miller, S. S., Mocanu, P. T., Differential Subordination Theory and Applications Series on Monographs and Textbooks in Pure and Applied Mathematics, Vol. 225, Marcel Dekker Inc., New York, 2000.
CR  - Mahmood, S., Ahmed, q. Z., Srivastava, H. M., Khan, N., Khan, B., Tahir, M., A certain subclass of meromorphically q-starlike functions associated with the Janowski function, J. Inequal. Appl. Math., 2019(88) (2019), 1-11. https://doi.org/10.1186/s13660-019-2020-z
CR  - Naeem, M., Hussain, S., Sakar, F. M., Mahmood T., Rasheed, A., Subclasses of uniformly convex and starlike functions associated with Bessel functions, Turkish Journal of Mathematics, 
2019(43) (2019), 2433-2443. DOI:10.3906/mat-1905-27
CR  - Owa, s., Srivastava, H. M., Current Topics in Analytic Function Theory, World Scientific, Singapore, 1992. https://doi.org/10.1142/1628
CR  - Pommerenke, C., On meromorphic starlike functions. Pac. J. Math., 13 (1963), 221–235.
CR  - Rasheed, A., Hussain, S., Shah, S. G. A., Darus, M., Lodhi, S., Majorization problem for two subclasses of meromorphic functions associated with a convolution operator, AIMS Mathematics,
5(5) (2020), 5157–5170. doi: 10.3934/math.2020331
CR  - Srivastava, H. M., Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A: Sci., 44(2020) (2020), 327–344.
CR  - Srivastava, H. M., Tahir, M., Khan, B., Ahmad, Q. Z., Khan, N., Some general families of q-starlike functions associated with the Janowski functions, Filomat, 33(9) (2019), 2613–2626.
https://doi.org/10.2298/FIL1909613S
CR  - Shah, S. G. A., Hussain, S., Rasheed, A., Shareef, Z., Darus, M., Application of quasi subordination to certain classes of meromorphic functions, Journal of Function Spaces, Vol. (2020), Article ID 4581926, 8 pages. https://doi.org/10.1155/2020/4581926
CR  - Srivastava, H. M., Hossen, H. M., Aouf, M, K., A unified presentation of some classes of meromorphically multivalent functions, Comput. Math. Appl., 38(11-12), (1999), 63-70.
CR  - Srivastava, H. M., Bansal, D., Close-to-convexity of a certain family of q-Mittag-Leffler functions, J. Nonlinear Var. Anal., 1 (2017), 61–69.
CR  - Srivastava, H. M., Tahir, M., Khan, B., Ahmed, Q. Z., Khan, N., Some general classes of q-starlike functions associated with the Janowski function, Symmetry, 11 (2019), Article ID 292, 1-14. DOI:10.3390/sym11020292
CR  - Swaminathan, K., Raghavendar, A close-to-convexi of basic hypergeometric functions using their Taylor coefficients, J. Math. Appl., 35 (2012), 111–125.
CR  - Shah, S. G. A., Noor, S., Darus, M., W. Ul Haq, S. Hussain, On meromorphic functions defined by a new class of liu-srivastava integral operator, International Journal of Analysis and Applications, 18(6) (2020), 1056-1065.
CR  - Wongsaijai, B., Sukantamala, N., Certain properties of some families of generalized starlike functions with respect to q-calculus. Abstr. Appl. Anal., (2016), 1-8. https://doi.org/10.1155/2016/6180140
UR  - https://doi.org/10.31801/cfsuasmas.883970
L1  - https://dergipark.org.tr/en/download/article-file/1591099
ER  -