Hankel determinant for the class of bounded turning functions associated with generalized telephone numbers

Trailokya  Panigrahi; Gangadharan  Murugusundaramoorthy

doi:10.5269/bspm.62379

T. Panigrahi https://orcid.org/0000-0001-7289-9578
Gangadharan Murugusundaramoorthy G.Murugusundaramoorthy,Ph.DSr.Professor of Mathematics,School of Advanced Sciences,VIT UNIVERSITY,Vellore-632 014

Abstract

In the present paper making use of subordination between two analytic functions, certain subclass of bounded turning functions associated with generalized telephone numbers is
introduced. The few coefficients bounds are obtained through series expansion and later used to investigate the optimum bounds of the Hankel determinant of order three for above defined class.

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Author Biographies

T. Panigrahi

Institute of Mathematics and Applications,\\ Andharua,
Bhubaneswar-751029,Odisha, India

Gangadharan Murugusundaramoorthy, G.Murugusundaramoorthy,Ph.DSr.Professor of Mathematics,School of Advanced Sciences,VIT UNIVERSITY,Vellore-632 014

G.Murugusundaramoorthy,Ph.D

Sr.Professor of Mathematics,

School of Advanced Sciences,

VIT UNIVERSITY,Vellore-632 014

References

Altinkaya, S.and Yalcin,S. Third Hankel determinant for Bazilevic functions,Advance Math., 5, 91-96,(2016).

Arif,M., Raza,M., Tang,H., Hussain, S.and Khan,H. Hankel determinant of order three for familiar subsets of analytic functions related with sine function, Open Math., 17(1), 1615-1630,(2019).

Babalola,K. O. On H3(1) Hankel determinant for some classes of univalent functions, Inequal. Theory Appl. 6, 1-7,(2010). ID: 22.

Bednarz, U. and Wolowiec-Musial,M. On a new generalization of telephone numbers, Turk. J. Math., 43, 1595-1603,(2019).

Cho,N. E., Kumar,V., Kumar, S. S. and Ravichandran,V. Radius problems for starlike functions associated with the sine function, Bull. Iran. Math. Soc., 45, 213-232,(2019).

Cho,N. E. Kumar,S., Kumar,V., Ravichandran, V. and Srivastava,M. H.Starlike functions related to the Bell numbers, Symmetry, 11(2), Doi:10.3390/sym11020219(2019).

Deniz,E. Sharp coefficient bounds for starlike functions associated with generalized telephone numbers, Bull Malays. Math. Sci. Soc., Springer, 18 pages(2020).

Dziok,J. Raina, R. K. and Sokol,J. On a class of starlike functions related to a shell-like curve connected with Fibonacci numbers, Math. Comput. Model, 57, 1203-1211,(2013).

Jangteng,A., Halim S. A. and Darus,M.Coefficient inequality for a function whose derivative has a positive real part, J. Ineq. Pure Appl. Math., 7, 1-5,(2006).

Jangteng,A., Halim S. A. and Darus,M. Coefficient inequality for starlike and convex functions,Int. J. Ineq. Math. Anal, 1, 619-625,(2007).

Janowski,W. Extremal problems for a family of functions with positive real part and for some related families,Ann. Polon. Math., 23, 159-177,(1970).

Keough, F. and Merkes,E. A coefficient inequality for certain subclasses of analytic functions, Proc. Amer. Math. Soc., 20, 8-12,(1969).

Krishna,D. V., Venkateswarlua, B. and RamReddy,T. Third Hankel determinant for bounded turning functions of order alpha, J. Niger. Math Soc., 34(2015), 121-127.

Kumar, S. and Ravichandran,V. A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math., 40, 199-212,(2016).

Kwon,O. S. Lecko, A. and Sim, Y. J.The bound of the Hankel determinant of the third kind for starlike functions, Bull. Malays. Math. Sci. Soc., 42 , 1-14,(2018).

Lecko,A., Sim Y. J. and Smiarowska, B. The sharp bound of the Hankel determinant of the third kind for starlike functions of order 12 , Complex. Anal. Oper. Theory, 13(5), 2231-2238,(2019).

Mendiratta,R., Negpal, S. and Ravichandran,V. On a subclass of strongly starlike functions associated with exponential function, Bull. Malays. Math. Sci. Soc., 38, 365-386,(2015).

Mohapatra, R. N. and Panigrahi,T. Second Hankel determinant for a class of analytic functions defined by Komatu integral operator, Rend. Mat. Appl., ,41(1), 51-58,(2020) .

Murugusundaramoorthy, G. andVijaya,K. Certain subclasses of analytic functions associated with generalized telephone numbers. Symmetry, 14, 1053 (2022). https://doi.org/10.3390/sym14051053

Naik, A. and Panigrahi,T. Upper bound on Hankel determinant for bounded turning function associated with Salageandifference operator, Survey Math Appl., 15, 525-543,(2020).

Panigrahi, T. and Jena,L. Upper bound of second Hankel determinant for generalized Sakaguchi-type spiral like functions, Bol. Soc. Paran. Math.,35(3), 263-272,(2017).

Pommerenke,C. On the coefficients and Hankel determinants of univalent functions, J. London Math. Soc., 41(1), 111-122,(1966).

Pommerenke, C.On the Hankel determinants of univalent functions, Mathematika, 14(1), 108-112,(1967).

Pommerenke,C. Univalent Functions, Studia Mathematica/Mathematische Lehrbucher, 25, Vandenhoeck and Ruprecht, Gottingen, 1975.

Raina R. K. and Sokol,J. Some properties related to a certain class of starlike functions, C. R. Math. Acad. Sci. Paris, 353(11), 973-978(2015).

Sokol, J. and Stankiewicz, J. Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat., 19, 101-105,(1996).

Zaprawa, P.,Third Hankel determinants for subclasses of univalent functions, Mediterr. J. Math., 14(1), 10 pages(2017).