Research Article
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Year 2022, Volume: 71 Issue: 1, 25 - 38, 30.03.2022

F. Müge Sakar Syed Ghoos Ali Shah Saqib Hussain Akhter Rasheed Muhammad Naeem

https://doi.org/10.31801/cfsuasmas.883970
Cited By: 2

Abstract

References

  • Aouf, M. K., Silverman, H., Partial sums of certain meromorphic p-valent functions, J. Inequal. Pure Appl. Math., 7(4), Article 119, (2006).
  • Aral, A., Gupta, V., Agarwal, R. P., Applications of q-Calculus in Operator Theory, Springer, New York, USA, 2013.
  • 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
  • Clunie, J., On meromorphic schlicht functions, J. London Math. Soc., 34 (1959), 215-216.
  • Darus, M., Hussain, S., Raza, M., Sokol, J., On a subclass of starlike functions, Results in Mathematics, 73 (2018), 1-12.
  • Gasper, G., Rahman, M., Basic Hypergeometric Series, Cambridge University Press Cambridge, 1990.
  • 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.
  • Ismail, M. E. H., Merkes, E., Styer, D., A generalization of starlike functions, Complex Var. Theory Appl., 14 (1990), 77-84.
  • Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193–203.
  • Jackson, F. H., q-difference equations, Am. J. Math., 32 (1910), 305–314.
  • Janowski, W., Some extrenal problems for certain families of analytic functions, Ann. Pol. Math., 28 (1973), 297–326.
  • 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
  • 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
  • Miller, J. E., Convex meromrphic mapping and related functions, Proc. Amer. Math. Soc., 25 (1970), 220-228.
  • Miller, S. S., Mocanu, P. T., Differential subordination and univalent functions, Mich. Math. J., 28 (1918), 157–171.
  • 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.
  • 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
  • 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
  • Owa, s., Srivastava, H. M., Current Topics in Analytic Function Theory, World Scientific, Singapore, 1992. https://doi.org/10.1142/1628
  • Pommerenke, C., On meromorphic starlike functions. Pac. J. Math., 13 (1963), 221–235.
  • 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
  • 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.
  • 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
  • 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
  • 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.
  • 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.
  • 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
  • Swaminathan, K., Raghavendar, A close-to-convexi of basic hypergeometric functions using their Taylor coefficients, J. Math. Appl., 35 (2012), 111–125.
  • 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.
  • 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

q-Meromorphic closed-to-convex functions related with Janowski function

Year 2022, Volume: 71 Issue: 1, 25 - 38, 30.03.2022

F. Müge Sakar Syed Ghoos Ali Shah Saqib Hussain Akhter Rasheed Muhammad Naeem

https://doi.org/10.31801/cfsuasmas.883970
Cited By: 2

Abstract

In the present paper, we introduce and explore certain new classes of meromorphic functions related with closed-to-convexity and q-calculus. Such results as
coefficient estimates, grow the property and partial sums are derived. It is important to mentioned that our results are generalization of number of existing
results in literature.

Keywords

Meromorphic starlike function Janowski functions q-derivative

References

  • Aouf, M. K., Silverman, H., Partial sums of certain meromorphic p-valent functions, J. Inequal. Pure Appl. Math., 7(4), Article 119, (2006).
  • Aral, A., Gupta, V., Agarwal, R. P., Applications of q-Calculus in Operator Theory, Springer, New York, USA, 2013.
  • 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
  • Clunie, J., On meromorphic schlicht functions, J. London Math. Soc., 34 (1959), 215-216.
  • Darus, M., Hussain, S., Raza, M., Sokol, J., On a subclass of starlike functions, Results in Mathematics, 73 (2018), 1-12.
  • Gasper, G., Rahman, M., Basic Hypergeometric Series, Cambridge University Press Cambridge, 1990.
  • 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.
  • Ismail, M. E. H., Merkes, E., Styer, D., A generalization of starlike functions, Complex Var. Theory Appl., 14 (1990), 77-84.
  • Jackson, F. H., On q-definite integrals, Quart. J. Pure Appl. Math., 41 (1910), 193–203.
  • Jackson, F. H., q-difference equations, Am. J. Math., 32 (1910), 305–314.
  • Janowski, W., Some extrenal problems for certain families of analytic functions, Ann. Pol. Math., 28 (1973), 297–326.
  • 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
  • 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
  • Miller, J. E., Convex meromrphic mapping and related functions, Proc. Amer. Math. Soc., 25 (1970), 220-228.
  • Miller, S. S., Mocanu, P. T., Differential subordination and univalent functions, Mich. Math. J., 28 (1918), 157–171.
  • 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.
  • 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
  • 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
  • Owa, s., Srivastava, H. M., Current Topics in Analytic Function Theory, World Scientific, Singapore, 1992. https://doi.org/10.1142/1628
  • Pommerenke, C., On meromorphic starlike functions. Pac. J. Math., 13 (1963), 221–235.
  • 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
  • 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.
  • 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
  • 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
  • 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.
  • 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.
  • 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
  • Swaminathan, K., Raghavendar, A close-to-convexi of basic hypergeometric functions using their Taylor coefficients, J. Math. Appl., 35 (2012), 111–125.
  • 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.
  • 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
There are 30 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

F. Müge Sakar 0000-0002-3884-3957

Syed Ghoos Ali Shah This is me 0000-0003-4283-8058

Saqib Hussain 0000-0002-8174-8795

Akhter Rasheed This is me 0000-0003-3810-5214

Muhammad Naeem 0000-0002-9069-3095

Publication Date March 30, 2022
Submission Date February 23, 2021
Acceptance Date July 7, 2021
Published in Issue Year 2022 Volume: 71 Issue: 1

Cite

APA Sakar, F. M., Shah, S. G. A., Hussain, S., Rasheed, A., et al. (2022). q-Meromorphic closed-to-convex functions related with Janowski function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(1), 25-38. https://doi.org/10.31801/cfsuasmas.883970
AMA Sakar FM, Shah SGA, Hussain S, Rasheed A, Naeem M. q-Meromorphic closed-to-convex functions related with Janowski function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. March 2022;71(1):25-38. doi:10.31801/cfsuasmas.883970
Chicago Sakar, F. Müge, Syed Ghoos Ali Shah, Saqib Hussain, Akhter Rasheed, and Muhammad Naeem. “Q-Meromorphic Closed-to-Convex Functions Related With Janowski Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 1 (March 2022): 25-38. https://doi.org/10.31801/cfsuasmas.883970.
EndNote Sakar FM, Shah SGA, Hussain S, Rasheed A, Naeem M (March 1, 2022) q-Meromorphic closed-to-convex functions related with Janowski function. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 1 25–38.
IEEE F. M. Sakar, S. G. A. Shah, S. Hussain, A. Rasheed, and M. Naeem, “q-Meromorphic closed-to-convex functions related with Janowski function”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 1, pp. 25–38, 2022, doi: 10.31801/cfsuasmas.883970.
ISNAD Sakar, F. Müge et al. “Q-Meromorphic Closed-to-Convex Functions Related With Janowski Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/1 (March 2022), 25-38. https://doi.org/10.31801/cfsuasmas.883970.
JAMA Sakar FM, Shah SGA, Hussain S, Rasheed A, Naeem M. q-Meromorphic closed-to-convex functions related with Janowski function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:25–38.
MLA Sakar, F. Müge et al. “Q-Meromorphic Closed-to-Convex Functions Related With Janowski Function”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 1, 2022, pp. 25-38, doi:10.31801/cfsuasmas.883970.
Vancouver Sakar FM, Shah SGA, Hussain S, Rasheed A, Naeem M. q-Meromorphic closed-to-convex functions related with Janowski function. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(1):25-38.

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Certain Class of Close-to-Convex Univalent Functions
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Univalence and Starlikeness of Certain Classes of Analytic Functions
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https://doi.org/10.3390/sym15051014

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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