
تعداد نشریات | 21 |
تعداد شمارهها | 610 |
تعداد مقالات | 9,028 |
تعداد مشاهده مقاله | 67,082,838 |
تعداد دریافت فایل اصل مقاله | 7,656,341 |
The (p. q)-analogue of sigmoid function in the mirror of bi-univalent functions coupled with subordination | ||
International Journal of Nonlinear Analysis and Applications | ||
مقاله 78، دوره 13، شماره 2، مهر 2022، صفحه 953-961 اصل مقاله (422.92 K) | ||
نوع مقاله: Research Paper | ||
شناسه دیجیتال (DOI): 10.22075/ijnaa.2021.21063.2227 | ||
نویسندگان | ||
S. O. Olatunji1؛ Trailokya Panigrahi* 2 | ||
1Department of Mathematical Sciences, Federal University of Technology, P.M.B.704, Akure, Nigeria | ||
2Institute of Mathematics and Applications, Andharua, Bhubaneswar-751029, Odisha, India | ||
تاریخ دریافت: 17 مرداد 1399، تاریخ بازنگری: 17 اسفند 1399، تاریخ پذیرش: 23 فروردین 1400 | ||
چکیده | ||
The aim of this study is to introduce the new subclasses of bi-univalent functions coupled with subordination in the mirror of $(p,q)$-analogue of the modified sigmoid function in the unit disc $\mathbb{U}=\left\lbrace z\in \mathbb{C}:|z|<1\right\rbrace $. The first two immediate Taylor-Maclaurin coefficients for the function belonging to these newly introduced classes are obtained. The results are new and a number of corollaries are developed by varying the parameters involved. | ||
کلیدواژهها | ||
Analytic function؛ Bi-univalent function؛ Coefficient bounds؛ (p؛ q)-analogue of the sigmoid function | ||
مراجع | ||
[1] T. Al-Hawary, F. Yousef and B.A. Frasin, Subclasses of analytic functions of complex order involving Jackson’s (p, q)-derivative, Proc. Int. Conf. Fractional Differ. Appl. (ICFDA), 2018. [2] K. Al-Shaqsi, On inclusion results of certain subclasses of analytic functions associated with generating function, AIP Conf, Proc. 1830(2017), no. 1, 1–6. [3] S. Altinkaya and S. Yalcin, Coefficient bounds for a subclass of bi-univalent functions, TWMS J. Pure Appl. Math. 6 (2015), no. 2, 180–185. [4] A. Arial, V. Gupta and R.P. Agarwal, Application of q-calculus in operator theory, Springer, New York, 2013. [5] D A. Brannan and J. G. Clunie(Eds.), Aspects of contemporary complex analysis (Proc. NATO Adv. Study Institute Held at the University of Durham, Durham: July 1-20, 1979), Academic Press, New York and London, 1980. [6] S. Bulut, N. Magesh and C. Abirami, A comprehensive class of analytic bi-univalent functions by means of Chebyshev polynomials, J. Frac. Cal. Appl. 8 (2017), no. 2, 32–39. [7] P.L. Duren, Univalent functions, Grundlehren der Mathematischen Wissenschaften, Band 259, Springer-Verlag, New York, Berlin, Heidelberg and Tokyo, 1983. [8] U.A. Ezeafulukwe, M. Darus and O.A. Fadipe-Joseph, The q-analogue of sigmoid function in the space of univalent λ−pseudo star-like function, Int. J. Math. Coput. Sci. 15 (2020), no. 2, 621–626. [9] E. Heine Uber die Reihe 1 + (qα−1)(qβ−1)(q−1)(qγ−1) z +(qα−1)(qα+1−1)(qβ−1)(qβ+1−1)(q−1)(q2−1)(qγ−1)(qγ+1−1) z2 + ..., J. Reine Angew. Math. 32 (1846), 210–212. [10] E. Heine Untersuchungen Uber die Reihe 1 + (qα−1)(qβ−1)(q−1)(qγ−1) z +(qα−1)(qα+1−1)(qβ−1)(qβ+1−1)(q−1)(q2−1)(qγ−1)(qγ+1−1) z2 +..., J. Reine Angew. Math. 34 (1847), 285–328. [11] O.A. Fadipe-Joseph, A.T. Oladipo and U.A. Ezeafulukwe, Modified sigmoid function in univalent function theory, Int. J. Math. Sci. Eng. Appl. 7 (2013), 313–317. [12] D.S. Kim and T.K. Kim, q−Bernoulli polynomials and q−umbral calculus, Sci. China Math. 57 (2014), 1867–1874. [13] M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63–68. [14] S.S. Miller and P.T. Mocanu, Differential Subordinations: Theory and Applications, Series on Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York and Basel, 2000. [15] G. Murugusundaramoorthy and T. Janani, Sigmoid function in the space of univalent λ-pseudo starlike functions, Int. J. Pure Appl. Math. Sci. 101 (2015), 33–41. [16] E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |z| < 1, Arch. Rational Mech. Anal. 32 (1969), 100–112. [17] S.O. Olatunji, Sigmoid function in the space of univalent λ-pseudo starlike function with Sakaguchi type functions, J. Progr. Res. Math. 7(2016), 1164-1172. [18] T. Panigrahi, Coefficient bounds for certain subclasses of meromorphic and bi-univalent functions, Bull. Korean Math. Soc., 50 (2013), no. 5, 1531–1538. [19] T. Panigrahi, A certain new class of analytic functions associated with quasi-subordination in the space of modified sigmoid functions, Analele Univ. Oradea Fasc. Mat. Tom XXV (2018), no. 2, 77–83. [20] T. Panigrahi and G. Murugusundaramoorthy, Coefficient bounds for bi-univalent analytic functions associated with Hohlov operator, Proced. Jangjeon Math. Soc. 16 (2013), no. 1, 91–100. [21] H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of anlaytic and bi-univalent functions, Appl. Math. Lett. 23 (2010), 1188–1192. [22] J. Touchard, Sur les cycles des substitutions, Acta Math. 70 (1939), no. 1, 243–297. [23] A.T. Yousef and Z. Salleh, A generalized subclass of starlike functions involving Jackson’s (p, q)-derivative, Iraqi J. Sci. 61 (2020), no. 3, 625–635. | ||
آمار تعداد مشاهده مقاله: 43,969 تعداد دریافت فایل اصل مقاله: 435 |