Kendisi ve Tersi Yalınkat Fonksiyonların Balans Polinomları ile Tanımlanan Bazı Yeni Alt Sınıfları Üzerine

Year 2023, , 25 - 32, 30.06.2023

İbrahim Aktaş , İnci Karaman

https://doi.org/10.55213/kmujens.1252471

Cited By: 3

Abstract

Bu makalede, Balans polinomları kullanılarak kendisi ve tersi yalınkat olan analitik fonksiyonların iki yeni alt sınıfı tanıtılmıştır. Daha sonra, bu yeni sınıflara ait fonksiyonların ilk iki Taylor-Maclaurin katsayıları için katsayı tahminleri belirlenmiştir. Son olarak, tanımlanan sınıflardaki fonksiyonlar i¸cin Fekete-Szegö problemi ele alınıp incelenmiştir

Keywords

Balans polinomları, Bi-¨univalent fonksiyon, katsayı tahminleri, Fekete-Szeg¨o fonksiyoneli.

On some new subclasses of bi-univalent functions defined by Balancing polynomials

Abstract

In this paper, two new subclasses of holomorphic and bi-univalent functions are introduced by using Balancing polynomials. Then, coefficient estmations are determined for the first two coefficients of functions belonging to these new classses. Finally, the Fekete-Szeg¨o problem is handled for the functions in subclasses defined.

Keywords

Balancing polynomials, Bi-univalent function, coefficient estimates, Fekete-Szeg\"{o} functional

References

• Behera A., Panda GK., On the square roots of triangular numbers, Fibonacci Quart., 37, 98–105, (1999).
• Brannan D., Clunie J., Aspects of contemporary complex analysis, Academic Press, New York, (1980).
• Brannan D., Taha TS., On some classes of bi-univalent functions, In: Proceedings of the International Conference on Mathematical Analysis and its Applications, Math. Anal. Appl., 53–60, (1988).
• Buyankara M., C¸ a˘glar M., Cotˆırl˘a LI., New Subclasses of Bi-Univalent Functions with Respect to the Symmetric Points Defined by Bernoulli Polynomials, Axioms, 11(11), Art. 652, (2022).
• Çağlar M., Cotˆırl˘a LI., Buyankara M., Fekete–Szeg¨o Inequalities for a New Subclass of Bi-Univalent Functions Associated with Gegenbauer Polynomials, Symmetry, 14(8), Art. 1572, (2022).
• Çağlar M., Chebyshev polynomial coefficient bounds for a subclass of bi-univalent functions, C. R. Acad. Bulgare Sci., 72, 1608–1615, (2019).
• Çağlar M., Orhan H., Ya˘gmur N., Coefficient bounds for new subclasses of bi-univalent functions, Filomat, 27, 1165–1171, (2013).
• Davala RK., Panda GK., On sum and ratio formulas for balancing numbers, J. Indian Math. Soc. (N.S.), 82(1-2), 23–32,(2015).
• Duren PL., Univalent Functions, In: Grundlehren der Mathematischen Wissenschaften, Band 259, New York, Berlin, Heidelberg and Tokyo, Springer-Verlag, (1983).
• Frasin BA., Swamy SR., Aldawish I., A comprehensive family of bi-univalent functions defined by k-Fibonacci numbers, J. Funct. Spaces, 2021, Art. 4249509, (2021).
• Frasin BA., Swamy SR., Nirmala J., Some special families of holomorphic and Al-Oboudi type bi-univalent functions related to k-Fibonacci numbers involving modified Sigmoid activation function, Afr. Math., 32, 631–643, (2021).
• Frontczak R., On balancing polynomials, Appl. Math. Sci., 13(2), 57–66, (2019).
• Frontczak R., Baden-W¨urttemberg L., A note on hybrid convolutions involving balancing and Lucas-balancing numbers, Appl. Math. Sci., 12(25), 2001–2008, (2018).
• Frontczak R., Baden-W¨urttemberg L., Sums of balancing and Lucas-balancing numbers with binomial coefficients,Int. J. Math. Anal., 12(12), 585–594, (2018).
• Güney HO., Murugusundaramoorthy G., Soko l J., Subclasses of bi-univalent functions related to shell-like curves ¨connected with Fibonacci numbers, Acta Univ. Sapientiae Math., 10, 70–84, (2018).
• Güney HO., Murugusundaramoorthy G., Soko l J., Certain subclasses of bi-univalent functions related to ¨ k-Fibonacci numbers, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68, 1909–1921, (2019).
• Keskin R., Karaatlı O., Some new properties of balancing numbers and square triangular numbers, J. Integer Seq.,15(1), 1–13, (2012).
• Komatsu T., Panda GK., On several kinds of sums of balancing numbers, arXiv:1608.05918, (2016).
• Lewin M., On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18, 63–68, (1967).
• Miller SS., Mocanu PT., Differential Subordinations, Monographs and Textbooks in Pure and Applied Mathematics,225, Marcel Dekker, Inc., New York, (2000).
• Orhan H., Toklu E., Kadıo˘glu E., Second Hankel determinant for certain subclasses of bi-univalent functions involving Chebyshev polynomials, Turkish J. Math., 42(4), 1927–1940, (2018).
• Patel BK., Irmak N., Ray PK., Incomplete balancing and Lucas-balancing numbers, Math. Rep., 20(70), 59–72, (2018).
• Ray PK., Some Congruences for Balancing and Lucas-Balancing Numbers and Their Applications, Integers, 14, A8,(2014).
• Ray PK., On the properties of k-balancing numbers, Ain Shams Engineering Journal, 9(3), 395–402, (2018).
• Ray PK., Balancing and Lucas-balancing sums by matrix methods, Math. Rep. (Bucur.), 17(2), 225–233, (2015).
• Srivastava HM., Mishra AK., Gochhayat P., Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett., 23, 1188–1192, (2010).
• Srivastava HM., Bulut S., C¸ a˘glar M., Ya˘gmur N., Coefficient estimates for a general subclass of analytic and biunivalent functions, Filomat, 27, 831–842, (2013).
• Toklu E., A new subclass of bi-univalent functions defined by q-derivative, TWMS J. of Apl. & Eng. Math., 9(1), 84–90, (2019).
• Toklu E., Aktaş İ., Sagsoz F., On new subclasses of bi-univalent functions defined by generalized S˘al˘agean differential operator, Commun. Fac. Sci. Univ. Ank. Ser. A1. Math. Stat., 68(1), 776-783, (2019).
• Zaprawa P., On the Fekete-Szeg¨o problem for classes of bi-univalent functions, Bull. Belg. Math. Soc. Simon Stevin, 21(1), 169–178, (2014).