Coefficient Inequalities for Certain Univalent Analytic Starlike And Convex Functions in Leaf Like Domain Through Jackson Q-Derivative Operator
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Two subclasses of starlike and convex functions analytic in the unit open disk using q-derivative operator have been investigated in the present paper. The necessary and sufficient condition for the function belonging to these classes have been obtained. We further examine various properties, such as the Hadamard product and the quasi-Hadamard product. The coefficient estimates for the function belonging to these classes are also found.
Mathematics Subject Classification 2020: 30C45, 30C50
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S. Agrawal and S. K. Sahoo. A generalization of starlike functions of order α. Hokkaido Mathematical Journal, 46(1):15–27, 2017. Zbl 1361.30017.
Abdullah Alsoboh, Ala Amourah, Omar Alnajar, Mamoon Ahmed, and Tamer M. Seoudy. Exploring q-fibonacci numbers in geometric function theory: Univalence and shell-like starlike curves. Mathematics, 13(8), 2025.
Abdullah Alsoboh and Georgia Irina Oros. A class of bi-univalent functions in a leaf-like domain defined through subordination via q-calculus. Mathematics, 12(10), 2024.
M. K. Aouf. The quasi-hadamard product of certain analytic functions. Applied Mathematics Letters, 21(11):1184–1187, 2008. MR2459845; Zbl 1159.30305.
M. K. Aouf, A. O. Mostafa, and H. M. Zayed. Convolution properties for some subclasses of meromorphic functions of complex order. Abstract and Applied Analysis, 2015:973613, 2015. Article ID 973613.
Mihai Aron. Coefficient estimates and fekete-szeg¨o problem for some classes of univalent functions generalized to a complex order. Demonstratio Mathematica, 58, 02 2025.
N. E. Cho, V. Kumar, S. S. Kumar, and V. Ravichandran. Radius problems for starlike functions associated with the sine function. Bulletin of the Iranian Mathematical Society, 45:213–232, 2019. Zbl 1409.30009.
H. E. Darwish. The quasi-hadamard product of certain starlike and convex functions. Applied Mathematics Letters, 20:692–695, 2007. Zbl 1111.30009.
R. M. El-Ashwah, M. K. Aouf, and N. Breaz. On quasi-hadamard products of p-valent functions with negative coefficients defined by using a differential operator. Acta Universitatis Apulensis. Mathematica Informatica, 28:61–70, 2011. Zbl 1274.30034.
B. A. Frasin and M. K. Aouf. Quasi-hadamard product of a generalized class of analytic and univalent functions. Applied Mathematics Letters, 23:347–350, 2010. Zbl 1186.30015.
G. Gasper and M. Rahman. Basic Hypergeometric Series. Cambridge University Press, Cambridge, 1990. Zbl 0695.33001.
H. M. Hossen. Quasi-hadamard product of certain p-valent functions. Demonstratio Mathematica, 33:277–281, 2000. Zbl 0963.30011.
F. H. Jackson. On q-definite integrals. Quarterly Journal, 41:193–203, 1910. JFM 41.0317.04.
F. H. Jackson. q-difference equations. American Journal of Mathematics, 32:305–314, 1910. MR1506108; JFM 41.0502.01.
W. Janowski. Extremal problems for a family of functions with positive real part and for some related families. Annales Polonici Mathematici, 23:159–177, 1970. Zbl 0199.39901.
S. Kant and P. P. Vyas. Convolution properties for certain subclasses of meromorphic p-valent functions. Journal of Fractional Calculus and Applications, 12(2):197–203, 2021. Zbl 1499.30102.
S. Kumar and A. C¸cetinkaya. Coefficient inequalities for certain starlike and convex functions. Hacettepe Journal of Mathematics and Statistics, 51(1):156– 171, 2022. Zbl 1499.30108.
S. S. Kumar and G. Kamaljeet. A cardioid domain and starlike functions. Analysis and Mathematical Physics, 11(2):35, 2021. Zbl 1461.30042.
V. Kumar. Hadamard product of certain starlike functions. Journal of Mathematical Analysis and Applications, 110:425–428, 1985. Zbl 0585.30013.
V. Kumar. Quasi-hadamard product of certain univalent functions. Journal of Mathematical Analysis and Applications, 126:70–77, 1987. Zbl 0625.30014.
W. C. Ma and D. Minda. A unified treatment of some special classes of univalent functions. In Conference Proceedings, Lecture Notes in Analysis, volume 1, pages 157–169, 1994. Zbl 0823.30007.
O. Mostafa, M. K. Aouf, H. M. Zayed, and T. Bulboac˘a. Convolution conditions for subclasses of meromorphic functions of complex order associated with basic bessel functions. Journal of the Egyptian Mathematical Society, 25(3):286–290, 2017. Zbl 1376.30009.
S. Owa. On the classes of univalent functions with negative coefficients. Mathematica Japonica, 27:409–416, 1982. Zbl 0497.30015.
S. Owa. On the hadamard products of univalent functions. Tamkang Journal of Mathematics, 14:15–21, 1983. Zbl 0527.30001.
S. Ponnusamy. Convolution properties of some classes of meromorphic univalent functions. Proceedings of the Indian Academy of Sciences. Mathematical Sciences, 103(1):73–89, 1993. Zbl 0772.30017.
S. D. Purohit and R. K. Raina. Certain subclasses of analytic functions associated with fractional q-calculus operators. Mathematica Scandinavica, 109:55–70, 2011. Zbl 1229.33027.
V. Ravichandran, S. S. Kumar, and K. G. Subramanian. Convolution conditions for spirallikeness and convex spirallikeness of certain meromorphic p-valent functions. Journal of Inequalities in Pure and Applied Mathematics, 5(1):Article 7, 2004. Zbl 1062.30017.
T. Sekine. On quasi-hadamard products of p-valent functions with negative coefficients. In H. M. Srivastava and S. Owa, editors, Univalent Functions, Fractional Calculus, and Their Applications, pages 317–328. Ellis Horwood / John Wiley, Chichester, 1989. Zbl 0683.00012.
T. M. Seoudy and M. K. Aouf. Convolution properties for certain classes of analytic functions defined by q-derivative operator. Abstract and Applied Analysis, 2014:Article ID 846719 (7 pages), 2014. MR3272218; Zbl 07023188.
K. Sharma, N. K. Jain, and V. Ravichandran. Starlike functions associated with a cardioid. Africa Mathematica, 27:923–939, 2016. Zbl 1352.30015.
L. Shi, H. M. Srivastava, N. E. Cho, and M. Arif. Sharp coefficient bounds for a subclass of bounded turning functions with a cardioid domain. Axioms, 12(8):775, 2023. DOI: 10.3390/axioms12080775.
J. Soklo and J. Stankiewicz. Radius of convexity of some subclasses of strongly starlike functions. Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka, 147:101–105, 1996. Zbl 0880.30014.
Soni, P. P. Vyas, and S. Kant. Convolution properties for certain subclasses of meromorphic p-valent functions by means of cassinian ovals. Facta Universitatis. Series Mathematics and Informatics, 38(1):25–30, 2023. Zbl 07742875.
H. M. Srivastava. Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis. Iranian Journal of Science and Technology, Transactions A: Science, 44:327–344, 2020.
H. M. Srivastava, M. Arif, and M. Raza. Convolution properties of meromorphically harmonic functions defined by a generalized convolution q-derivative operator. AIMS Mathematics, 6(6):5869–5885, 2021. DOI: 10.3934/math.2021347.
H. M. Srivastava, M. Tahir, B. Khan, M. Darus, N. Khan, and Q. Ahmad. Certain subclasses of meromorphically q-starlike functions associated with the q-derivative operators. Ukrainian Mathematical Journal, 73:1462–1477, 2022. Zbl 1492.30049; DOI: 10.1007/s11253-022-02005-5.
R. Srivastava and H. M. Zayed. Subclasses of analytic functions of complex order defined by q-derivative operator. Studia Universitatis Babes,-Bolyai Mathematica, 64(1):71–80, 2019. MR3928603; Zbl 1438.30099.
Wahid Ullah, Sarfraz Nawaz Malik, Daniel Breaz, and Luminita-Ioana Cotirla. On logarithmic coefficients for starlike functions related to the nephroid domain. AIMS Mathematics, 10(11):26905–26925, 2025.
P. P. Vyas. Convolution conditions for certain subclasses of meromorphic pvalent functions. Facta Universitatis, Series Mathematics and Informatics, 37(1):159–168, 2022. Zbl 1499.32008.
P. P. Vyas. Convolution conditions for certain subclasses of meromorphic p-valent functions. Facta Universitatis. Series Mathematics and Informatics, 37(1):159–168, 2022. Zbl 1499.32008.
L. A. Wani and A. Swaminathan. Starlike and convex functions associated with a nephroid domain. Bulletin of the Malaysian Mathematical Sciences Society, 44:79–104, 2021. Zbl 1461.30046.
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