Applying The Quasi-Hadamard Product For Some Multivalent Functions That Implicitly Contain The Generalized Komatu Integral Operator
DOI:
https://doi.org/10.32792/jeps.v15i3.701Keywords:
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.
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