Frontiers in Emerging Multidisciplinary Sciences

Open Access Peer Review International
Open Access

Geometric Properties of a Novel Subclass of Meromorphic Multivalent Functions Defined by a Linear Operator

4 Department of Mathematics, University of Padua, Italy
4 Laboratory of Complex Analysis, Sorbonne University, Paris, France

Abstract

The field of geometric function theory is significantly enriched by the study of meromorphic functions, particularly those that are multivalent. Operators play a crucial role in defining and investigating novel subclasses of these functions, allowing for a deeper understanding of their geometric properties such as starlikeness, convexity, and close-to-convexity. This paper introduces and rigorously examines a new subclass of meromorphic multivalent functions by employing a generalized linear operator. Building upon established principles of differential subordination and superordination, as well as fractional calculus, we derive several key characteristics of functions belonging to this subclass, including coefficient bounds, inclusion relationships with other known function classes, and conditions for multivalent starlikeness and convexity. The results presented here extend previous work in the area and provide new insights into the complex analytical behavior of these functions. These findings contribute to the broader understanding of mathematical operators' applications in complex analysis and offer a foundation for further research into related function spaces and their potential applications.

How to Cite

Prof. Marco Ricci, PhD, & Dr. Sophie Dubois. (2025). Geometric Properties of a Novel Subclass of Meromorphic Multivalent Functions Defined by a Linear Operator. Frontiers in Emerging Multidisciplinary Sciences, 2(02), 1–4. Retrieved from https://irjernet.com/index.php/fems/article/view/62

References

πŸ“„ Akgaul A. (2016), A new subclass of meromorphic functions defined by Hilbert space operator, Honam Mathematical J., 38(3), pp. 495-506. http://dx.doi.org/10.5831/HMJ.2016.38.3.495
πŸ“„ Atshan W. G., Alzopee L. A. & Alcheikh M. M. (2013), On Fractional Calculus Operators of a class of Meromorphic Multivalent Functions, Gen. Math. Notes, 18(2), pp. 92-103. https://www.emis.de/journals/GMN/yahoo_site_admin/assets/docs/8_GMN-3992-V18N2.329202946.pdf
πŸ“„ Atshan W. G. & Buti R. H. (2011), Fractional calculus of a class of negative coefficients defined by Hadamard product with Rafid-operator, European J. Pure Appl. Math, 4(2), 162-17. https://www.ejpam.com/index.php/ejpam/article/view/1174/197
πŸ“„ 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, 23(7), 1133–1142. https://www.m-hikari.com/ijma/ijma-2013/ijma-21-24-2013/atshanIJMA21-24-2013.pdf
πŸ“„ 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), 10452-1045. https://docsdrive.com/?pdf=medwelljournals/jeasci/2019/10452-10458.pdf
πŸ“„ Husien A. A. J. (2024), Results on the Hadamard-Simpson's inequalities, Nonlinear Functional Analysis and Applications, 29(1), pp.47-56. https://doi.org/10.22771/nfaa.2024.29.01.04
πŸ“„ Hussein S.K. & Jassim K.A. (2019), β€œOn A Class of Meromorphic Multivalent Functions Convoluted with Higher Derivatives of Fractional Calculus Operator, Iraqi Journal of Science, 60(10), pp.79-94. https://doi.org/10.24996/ijs.2024.65.3.22
πŸ“„ Liu J.L. & Srivastava H. M. (2001), A linear operator and associated families of meromorphically multivalent functions, J. Math. Anal. Appl., 259, 566-58. https://doi.org/10.1006/jmaa.2000.7430
πŸ“„ 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 J.Math. http://dx.doi.org/10.1142/S1793557114500612
πŸ“„ Newton G. to Math. (2023), Isaac Newton Institute, Cambridge, United Kingdom, Industrial Applications of Complex Analysis. https://gateway.newton.ac.uk/event/ofbw51
πŸ“„ Rosy T. & Varma S. S. (2013), On a subclass of meromorphic functions defined by Hilbert space operator, Hindawi Publishing Corporation Geometry, 2013, article ID 671826, 4 pages. https://doi.org/10.1155/2013/671826
πŸ“„ Wang Z. G., Sun Y. & Zhang Z. H. (2009), Certain classes of meromorphic multivalent functions, Comput. Math. Appl., 58, 1408-1417. https://doi.org/10.1016/j.camwa.2009.07.020
πŸ“„ Panigrahi T. (2015), A subclasses 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