Fourth Hankel and Toeplitz determinants for a subclass of analytic functions subordinate to 1+sin(z)

• Autorzy: Ganesh Koride , Rayaprolu Bharavi Sharma , Saroja Kasula , Yakaiah Koneti

Identyfikatory

DOI

10.14708/ma.v51i2.7238

Warianty tytułu

PL

Wyznaczniki Hankela i Toeplitza czwartego rzędu dla podklasy funkcji analitycznych podporządkowanych 1 + sin z

• Języki publikacji: EN

Abstrakty

EN

The purpose of the present paper is to determine the coefficient bounds, fourth Hankel determinants, Toeplitz determinants for the function f in a subclass of analytic functions subordinate to 1+sin(z). We also study the Fekete-Szegö inequality and Zalcman conjecture for functions in this class.

PL

Celem tego badania jest ustalenie oszacowań współczynników wyznaczników Hankela czwartego rzędu oraz wyznaczników Toeplitza dla funkcji należących do podklasy funkcji analitycznych podporządkowanych wyrażeniu 1 + sin z. Dodatkowo, analizujemy nierówność Fekete-Szegő-Szegő oraz hipotezę Zalcmana dla funkcji w tejże klasie.

Słowa kluczowe

EN

Holomorphic function; Convex function; Starlike function; Subordination; Hankel determinants; Toeplitz determinants

PL

Funkcja holomorficzna; funkcja wypukła; funkcja jednolistna; funkcja gwiaździsta; podporządkowanie; wyznacznik Hankela; wyznaczniki Toeplitza

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Mathematica Applicanda
• Rocznik: 2023
• Tom: Vol. 51, no. 2
• Strony: 321--338
• Opis fizyczny: Bibliogr. 29 poz., rys.

Twórcy

autor

Ganesh Koride

• Jyothishmathi Institute of Technology and Science Karimnagar, Telangana, 505527, INDIA

• https://orcid.org/0009-0009-7354-0378+

autor

Rayaprolu Bharavi Sharma

• Kakatiya University Department of Mathematics, Warangal, Telangana 506001, INDIA

• https://orcid.org/0000-0003-2814-9774

autor

Saroja Kasula

• Govt. Degree College for Women Gajwel, Siddipet, Telangana 506001, INDIA

• https://orcid.org/0009-0005-7706-4648+

autor

Yakaiah Koneti

• Mallareddy Engineering College for Women Maisammaguda, Dhulapally(post) Kompally, Secunderabad, Telangana 500100, INDIA

• https://orcid.org/0000-0002-5203-6094+

Bibliografia

• [1] M. Ali, D. K. Thomas, and A. Vasudevarao. Toeplitz determinants whose elements are the coefficients of analytic and univalent functions. Bull. Aust. Math. Soc., 97(2):253-264, 2018.
• [2] M. Arif, M. Raza, H. Tang, S. Hussain, and H. Khan. Hankel determinant of order three for familiar subsets of analytic functions related with sine function. Open Math., 17:1615-1630, 2019.
• [3] M. Arif, L. Rani, M. Raza, P. Zaprawa. Fourth Hankel Determinant for the Set of Star-Like Functions. Mathematical Problems in Engineering, vol. 2021, Article ID 6674010, 8 pages, 2021.
• [4] M. Arif, L. Rani, M. Raza, P. Zaprawa. Fourth Hankel Determinant for the family of functions with bounded turning. Bulletin of the Korean Mathematical Society, 55(6): 1703—1711, 2018.
• [5] K. Bano and M. Raza. Starlike functions associated with cosine functions. Bull. Iran. Math. Soc., 47(5):1513-1532, 2021.
• [6] S. Bulut, N. Magesh, V. K. Balaji. Initial bounds for analytic and biunivalent functions by means of Chebyshev polynomials. Journal of Classical Anal., 11(1): 83–89, 2017.
• [7] K. Ganesh, K. Bharavi Sharma, K. Rajya Laxmi. Third Hankel determinant for a class of functions with respect to symmetric points associated with exponential function. WSEAS Trans. Math., 19: 133–138, 2020
• [8] M. G. Khan, B. Ahmad, J. Sokół, Z. Muhammad, W. K. Mashwani, R. Chinram, and P. Petchkaew. Coefficient problems in a class of functions with bounded turning associated with Sine function. Eur. J. Pure Appl. Math., 14(1):53?64, 2021. doi: 10.29020/nybg.ejpam.v14i1.3902. MR 4313264.
• [9] B. Kowalczyk, A. Lecko, Y. J. Sim. The sharp bound of the Hankel determinant of the third kind for convex functions. Bull. Austr. Math. Soc., 97 435–445, 2018.
• [10] K. Bharavi Sharma, K. Rajya Laxmi. Second Hankel determinants for some subclasses of biunivalent functions associated with pseudo-starlike functions. J. Complex Anal., pages Art. ID 6476391, 9, 2017.
• [11] R.J. Libera and E.J. Złotkiewicz. Early coefficients of the inverse of a regular convex function. Proc. Am. Math. Soc., 85 –230, 1982.
• [12] W. Ma and D. Minda. A unified treatment of some special classes of univalent functions. In Proc. Conf. on Complex Analysis, June 19-23, 1992, pages 157-169. Nankai University, Institute of Mathematics, Tianjin, People's Republic of China; Internet. Press, Cambridge, 1994.
• [13] M.N.M. Pauzi, M. Darus, and S. Siregar. Second and third Hankel determinant for a class defined by generalized polylogarithm functions.TJMM, 10 (1), 31–41, 2018.
• [14] M. M. Motamedinezhad and R. Kargar. A note on the paper Tang et al. (2017, 2018). arXiv, math.CV(1908.01306):4p., 2019.
• [15] C. Pommerenke. Univalent functions. With a chapter on quadratic differentials by Gerd Jensen. Studia Mathematica/Mathematische Lehrbücher. Band XXV. Vandenhoeck & Ruprecht, Göttingen, Germany, 1975.
• [16] R. K. Raina, J. Sokol. On Coefficient estimates for a certain class of starlike functions. Haccettepe Journal Math. Stat. 44(6): 1427–1433, 2015.
• [17] C. Ramachandran and D. Kavitha. Toeplitz determinants for some subclasses of analytic functions. Glob. J. Pure and Appl. Math., 13(2):785-793, 2017.
• [18] P. Sahoo. Third Hankel determinant for a class of analytic univalent functions. Electron. J. Math. Anal. Appl., 6(1):322?329, 2018.
• [19] K. Bharavi Sharma, M. Haripriya. On a class of α-convex functions subordinate to a shell shaped region. J. Anal., 25(1): 99–105, 2017.
• [20] H. M. Srivastava, S. Altinkaya, S. Yalcin. Hankel determinant for a subclass of bi-univalent functions defined by using a symmetric q-derivative operator. Filomat, 32:503–516, 2018.
• [21] H. M. Srivastava, Q. Z. Ahmad, N. Khan, N. Khan, and B. Khan. Hankel and Toeplitz determinants for a subclass of q-starlike functions associated with a general conic domain. Mathematics, 7(2):181-215, 2019.
• [22] H. Tang, H. M. Srivastava, S.-H. Li, and G.-T. Deng. Majorization results for subclasses of starlike functions based on the sine and cosine functions. Bull. Iran. Math. Soc., 46(2):381-388, 2020.
• [23] H. Tang, H. M. Srivastava, S.-H. Li, and G.-T. Deng. Correction to:"Majorization results for subclasses of starlike functions based on the sine and cosine functions". Bull. Iran. Math. Soc., 46(2):389-391, 2020.
• [24] D. Thomas and S. Abdul Halim. Retracted article: Toeplitz matrices whose elements are the coefficients of starlike and close-to-convex functions. Bull. Malays. Math. Sci. Soc., 40:1781-1790, 2017.
• [25] D. Thomas and S. Abdul Halim. Retraction note to: Toeplitz matrices whose elements are the coefficients of starlike and close-to-convex functions. Bull. Malays. Math. Sci. Soc., 41:1151, 2018.
• [26] P. Zaprawa.On Hankel Determinant H2(3) for Univalent Functions. Results Math, 73(89), 2018.
• [27] P. Zaprawa. On coefficient problems for functions starlike with respect to symmetric points. Bol. Soc. Mat. Mex., 28(17), 2022.
• [28] H.-Y. Zhang and H. Tang. Fourth Toeplitz determinants for starlike functions defined by using the sine function. J. Funct. Spaces, 021:7, 2021.
• [29] H.-Y. Zhang and H. Tang. A study of fourth-order Hankel determinants for starlike functions connected with the sine function. J. Funct.Spaces, 2021:8, 2021.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).