Applying The Quasi-Hadamard Product For Some Multivalent Functions That Implicitly Contain The Generalized Komatu Integral Operator

Authors

  • Hazha Zirar Hussain Salahaddin University

DOI:

https://doi.org/10.32792/jeps.v15i3.701

Keywords:

Coefficient bounds, Komatu integral operator, Multivalent functions, Quasi-Hadamard, Unit disk.

Abstract

Discussing and studying the principal results of the quasi-Hadamard product is the core or primary goal of this paper, which we apply to some multivalent functions with negative coefficients. This is done by defining a distinct class of multivalent functions with negative coefficients using the generalized linear operator, which implicitly contains the generalized Komatu integral operator. We also present most important basic properties of this distinct class of coefficient bounds and some results of quasi-Hadamard product. It is worth noting that this paper is nothing but a generalization or continuation of what was presented by the distinguished researchers previously. I have mentioned some of these previous studies related to the subject as precisely as I can. Let us not forget that all our work is within the famous unit disc .

References

Khairnar, S. M., & More, M. (2009). On a subclass of multivalent β-uniformly starlike and convex functions defined by a linear operator. IAENG Int. J. Appl. Math, 39(3), 1-9. https://doi.org/MR 2554929Zbl 1229.30008

Salim, T. O. (2010). A class of multivalent functions involving a generalized linear operator and subordination. Int. J. Open Problems Complex Analysis, 2(2), 82-94.

Saleh, Z. M., & Moustafa, A. O. (2024). A class of Multivalent Meromorphic Functions Involving an Integral Operator. Journal of Fractional Calculus and Applications, 15(2), 1-6. https://dx.doi.org/10.21608/jfca.2024.290678.1104

Hari, N., Nataraj, C., Reddy, P. T., & Kumar, S. S. (2025). Some Properties of Analytic Functions Associated with Erdély-Kober Integral Operator. Contemporary Mathematics, 2339-2354. https://doi.org/10.37256/cm.6220256033

Choi, J. H. (2025). Subordination by Certain Multivalent Functions Associated with Fractional Integral Operator. Journal of Applied Mathematics and Physics, 13(4), 1073-1084. https://doi.org/10.4236/jamp.2025.134055

Munasser, B. M., Mostafa, A. O., Sultan, T., EI-Sherbeny, N. A., & Madian, S. M. (2024). Inclusion Properties for Classes of p‐Valent Functions. Journal of Function Spaces, 2024(1), 2701156. https://doi.org/10.1155/2024/2701156

Marrero, I. (2025). A Class of Meromorphic Multivalent Functions with Negative Coefficients Defined by a Ruscheweyh-Type Operator. Axioms, 14(4), 284. https://doi.org/10.3390/axioms14040284

Salim, T. O. (2012), Integral properties of certain subclasses of multivalent functions with complex orde, Tamkang Journal of Mathematics, 3(2), 251-257.

Raina, R. K., & Bapna, I. B. (2009). On the Starlikeness and Convexity of a Certain Integral Operator. Southeast Asian Bulletin of Mathematics, 33(1), https://doi.org/101-108.MR 2481938Zbl 1212. 30066

Ebadian, A., Shams, S., Wang, Z. G., & Sun, Y. (2009). A class of multivalent analytic functions involving the generalized Jung-Kim-Srivastava operator. Acta Universitatis Apulensis. Mathematics-Informatics, 18, 265-277.

Bernardi, S. D. (1969). Convex and starlike univalent functions. Transactions of the American Mathematical society, 135, 429-446. https://doi.org/10.2307/1995025

Ebadian, A., & Najafzadeh, S. (2009). Uniformly starlike and convex univalent functions by using certain integral operators. Acta Universitatis Apulensis. Mathematics-Informatics, 20, 17-23. https://doi.org/MR 2656769Zbl1224.30046

Al-Oboudi, F. M. (2004). On univalent functions defined by a generalized Sălăgean operator. International Journal of Mathematics and Mathematical Sciences, 2004(27), 1429-1436https://doi.org/10.1155/S0161171204108090

Salagean, G. S. (2006, August). Subclasses of univalent functions. In Complex Analysis—Fifth Romanian-Finnish Seminar: Part 1 Proceedings of the Seminar held in Bucharest, June 28–July 3, 1981 (pp. 362-372). Berlin, Heidelberg: Springer Berlin Heidelberg. https://doi.org/10.1007/BFb0066543

Owa, S. and Aouf, M. K. (1994), On radii starlikeness and convexity for p-valent functions with negative coefficients, J. Fac. Sci. Tech. Kinki Univ., 30, 19-24.

Aouf, M. K. (1994). A Subclass of analytic p-valent functions with negative coefficients. 1. Utilitas Mathematica, 46, 219-231.

Sekine, T., & Owa, S. (1985). Note on a class of functions whose derivative has a positive real part. Bull. Soc. Royale Sci. Liege, 54, 203-210.

Owa, S. (1984). On a class of analytic functions with fixed second coefficients II. Bulletin de la Société Royale des Sciences de Liège. 719-730. https://doi.org/10.1155/S0161171284000752

Hasoon, I. A., & Al-Ziadi, N. A. J. (2024). New Class of Multivalent Functions Defined by Generalized (p, q)-Bernard Integral Operator. Earthline Journal of Mathematical Sciences, 14(5), 1091-1118. https://doi.org/10.34198/ejms.14524.10911118

Alshehri, F. A., Badghaish, A. O., Bajamal, A. Z., & Lashin, A. M. Y. (2025). A study on certain classes of multivalent analytic functions with fixed second coefficients. Communications of the Korean Mathematical Society, 40(1), 181-193. https://doi.org/10.4134/CKMS.c240106

Saleh, Z. M., & Mostafa, A. O. (2025). Convolution Results for Subclasses of Multivalent Meromorphic Functions of Complex Order Involving an Integral Operator. Electronic Journal of Mathematical Analysis and Applications, 13(2), 1-7.https://dx.doi.org/10.21608/ejmaa.2025.355261.1315

Pandey, A. K., Parida, L., Sahoo, A. K., Barik, S., & Paikray, S. K. (2025). On certain subclass of multivalent functions associated with Bessel functions. Integral Transforms and Special Functions, 1-17.https://doi.org/10.1080/10652469.2025.2460011

Wanas, A. K., Muthiayan, E., & Wanas, E. K. (2025). Applications of Fractional Calculus and Borel Distribution Series for Multivalent Functions on Complex Hilbert Space. Earthline Journal of Mathematical Sciences, 15(1), 11-21. https://doi.org/10.34198/ejms.15125.011021

YAGUCHI, T., KWON, O., CHO, N. E., & YAMAKAWA, R. (1993). A generalization class of certain subclasses of $ P $-valenty analytic functions with negative coefficients. 数理解析研究所講究録, 821, 101-111. https://doi.org/hdl.handle.net/2433/83190

Lee, S. K., Owa, S., & Srivastava, H. M. (1987). Basic properties and characterizations of a certain class of analytic functions with negative coefficients, Utilitas Math. 36, 121-128.

Downloads

Published

2025-09-01

Issue

Vol. 15 No. 3 (2025): JOURNAL OF EDUCATION FOR PURE SCIENCE

Section

Articles

License

Copyright (c) 2025 Journal of Education for Pure Science

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Copyright Policy

Authors retain copyright of their articles published in the Journal of Education for Pure Science (JEPS).

By submitting their work, authors grant the journal a non-exclusive license to publish, distribute, and archive the article in all formats and media.

License

All articles published in JEPS are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).

This license permits unrestricted use, distribution, and reproduction in any medium, provided that the original author(s) and the source are properly credited.

Author Rights

Authors have the right to:

  • Share their articles on personal websites, institutional repositories, and academic platforms

  • Reuse their work in future research and publications

  • Distribute the published version without restriction

Journal Rights

The journal retains the right to:

  • Publish and archive the articles

  • Include them in indexing and archiving systems such as LOCKSS and CLOCKSS

  • Promote and disseminate the published work

Responsibility

The contents of all articles are the sole responsibility of the authors. The journal, editors, and editorial board are not responsible for any errors, opinions, or statements expressed in the published articles.

Open Access Statement

JEPS provides immediate open access to its content, supporting the principle that making research freely available to the public enhances global knowledge exchange.

This work is licensed under a Creative Commons Attribution 4.0 International License.
https://creativecommons.org/licenses/by/4.0/