New properties of a subclass for a multivalent meromorphic functions with an operator
DOI:
https://doi.org/10.61856/4cq33h32Keywords:
multivalent meromorphic function, convolution properties, Rafid- operator, arithmetic mean, convex linear combinationsAbstract
We note in this study that we have calculated the Rafid- operator on the multivalent meromorphic functions that belong to the class and which is as in . On the punctured unit desk . Introduced defined a Rafid operator by (Atshan et al., (2011)) and also ( Rosy et al. (2013)) studied the same operator on the univalent meromorphic function. Now in this research we studied this operator on the multivalent meromorphic function and we obtain. if an operator which is as in defined , and after entering the operator on the above functions in , we get a new functions . We also introduce a new subclass for these functions with this operator and obtain the necessary and sufficient condition for functions to belong to this class. We also obtain new results for several properties of these functions in , including closed under arithmetic mean , closed under the combinations of convex linear and functions. These results are related to complex analysis in the theory of geometric functions.
References
Akgaul, A. (2016). A new subclass of meromorphic functions defined by Hilbert space operator. Honam Mathematical Journal, 38(3), 495–506. https://doi.org/10.5831/HMJ.2016.38.3.495
Atshan, W. G., Alzopee, L. A., & Alcheikh, M. M. (2013). On fractional calculus operators of a class of meromorphic multivalent functions. General Mathematics Notes, 18(2), 92–103. https://www.emis.de/journals/GMN/yahoo_site_admin/assets/docs/8_GMN-3992-V18N2.329202946.pdf
Atshan, W. G., & Buti, R. H. (2011). Fractional calculus of a class of negative coefficients defined by Hadamard product with Rafid operator. European Journal of Pure and Applied Mathematics, 4(2), 162–177. https://www.ejpam.com/index.php/ejpam/article/view/1174/197
Atshan, W. G., & Husien, A. A. J. (2013). Differential subordination of meromorphically p-valent analytic functions associated with Mostafa operator. International Journal of Mathematical Analysis, 7(23), 1133–1142. https://www.m-hikari.com/ijma/ijma-2013/ijma-21-24-2013/atshanIJMA21-24-2013.pdf
Husien, A. A. J. (2019). Differentiation subordination and superordination for univalent meromorphic functions involving Cho–Kwon–Srivastava operator. Journal of Engineering and Applied Sciences, 14(Special Issue), 10452–10458. https://docsdrive.com/pdfs/medwelljournals/jeasci/2019/10452-10458.pdf
Husien, A. A. J. (2024). Results on the Hadamard–Simpson inequalities. Nonlinear Functional Analysis and Applications, 29(1), 47–56. https://doi.org/10.22771/nfaa.2024.29.01.04
Hussein, S. K., & Jassim, K. A. (2019). On a class of meromorphic multivalent functions convoluted with higher derivatives of fractional calculus operator. Iraqi Journal of Science, 60(10), 79–94. https://doi.org/10.24996/ijs.2024.65.3.22
Liu, J.-L., & Srivastava, H. M. (2001). A linear operator and associated families of meromorphically multivalent functions. Journal of Mathematical Analysis and Applications, 259, 566–580. https://doi.org/10.1006/jmaa.2000.7430
Mishra, A. K., & Soren, M. M. (2014). Certain subclasses of multivalent meromorphic functions involving iterations of the Cho–Kwon–Srivastava transform and its combinations. Asian-European Journal of Mathematics. https://doi.org/10.1142/S1793557114500612
Newton, G. (2023). Industrial applications of complex analysis. Isaac Newton Institute for Mathematical Sciences, University of Cambridge. https://gateway.newton.ac.uk/event/ofbw51
Rosy, T., & Varma, S. S. (2013). On a subclass of meromorphic functions defined by Hilbert space operator. Geometry, 2013, Article ID 671826, 1–4. https://doi.org/10.1155/2013/671826
Wang, Z.-G., Sun, Y., & Zhang, Z.-H. (2009). Certain classes of meromorphic multivalent functions. Computers & Mathematics with Applications, 58, 1408–1417. https://doi.org/10.1016/j.camwa.2009.07.020
Panigrahi, T. (2015). A subclass of multivalent meromorphic functions associated with iterations of the Cho–Kwon–Srivastava operator. Palestine Journal of Mathematics, 4(1), 57–64. https://pjm.ppu.edu/sites/default/files/papers/7_3.pdf
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