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Year 2022, Volume: 51 Issue: 1, 156 - 171, 14.02.2022

Sushil Kumar Kumar , Asena Çetinkaya

https://doi.org/10.15672/hujms.778148
Cited By: 3

Abstract

References

  • [1] R.M. Ali, Coefficients of the inverse of strongly starlike functions, Bull. Malays. Math. Sci. Soc. 26 (1), 63-71, 2003.
  • [2] M.F. 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.
  • [3] M.K. Aouf, The quasi-Hadamard product of certain analytic functions, Appl. Math. Lett. 21, 1184-1187, 2008.
  • [4] K.O. Babalola, On H3(1) Hankel determinant for some classes of univalent functions, Ineq. Theory and Appl. 6, 1-7, 2010.
  • [5] N. Breaz and R.M. El-Ashwah, Quasi-Hadamard product of some uniformly analytic and p-valent functions with negative coefficients, Carpathian J. Math. 30 (1), 39-45, 2014.
  • [6] T. Bulboacă, M.K. Aouf and R.M. El-Ashwah, Convolution properties for subclasses of meromorphic univalent functions of complex order, Filomat 26 (1), 153-163, 2012.
  • [7] K. Cudna, O.S. Kwon, A. Lecko, Y.J. Sim and B. Śmiarowska, The second and third- order Hermitian Toeplitz determinants for starlike and convex functions of order , Bol. Soc. Mat. Mex. (3) 26 (2), 361-375, 2020.
  • [8] P.L. Duren, Univalent Functions, 259, Springer, New York, 1983.
  • [9] R.M. El-Ashwah, Some convolution and inclusion properties for subclasses of bounded univalent functions of complex order, Thai J. Math. 12 (2), 373-384, 2014.
  • [10] H. Güney, S. İlhan and J. Sokół, An upper bound for third Hankel determinant of starlike functions connected with k-Fibonacci numbers, Bol. Soc. Mat. Mex. (3) 25 (1), 117-129, 2019.
  • [11] W.K. Hayman, On the second Hankel determinant of mean univalent functions, Proc. London Math. Soc. (3) 18, 77-94, 1968.
  • [12] H.M. Hossen, Quasi-Hadamard product of certain p-valent functions, Demonstratio Math. 33 (2), 277-281, 2000.
  • [13] W. Janowski, Some extremal problems for certain families of analytic functions I, Ann. Polon. Math. 28, 297-326, 1973.
  • [14] P. Jastrz¸ebski B. Kowalczyk, Oh S. Kwon, A. Lecko and Y.J. Sim, Hermitian Toeplitz determinants of the second and third-order for classes of close-to-star functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (4), 166, 2020.
  • [15] W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1, 169-185, 1952.
  • [16] R. Kargar, A. Ebadian and J. Sokół, On Booth lemniscate and starlike functions, Anal. Math. Phys. 9 (1), 143-154, 2019.
  • [17] B. Kowalczyk, A. Lecko and Y.J. Sim, The sharp bound for the Hankel determinant of the third kind for convex functions, Bull. Aust. Math. Soc. 97 (3), 435-445, 2018.
  • [18] D. Kucerovsky, K. Mousavand and A. Sarraf, On some properties of Toeplitz matrices, Cogent Math. 3, 2016 (Article ID 1154705).
  • [19] V. Kumar, Hadamard product of certain starlike functions II, J. Math. Anal. Appl. 113, 230-234, 1986.
  • [20] V. Kumar, N. E. Cho, V. Ravichandran and H.M. Srivastava, Sharp coefficient bounds for starlike functions associated with the Bell numbers, Math. Slovaca 69 (5), 1053- 1064, 2019.
  • [21] V. Kumar and S. Kumar, Bounds on Hermitian-Toeplitz and Hankel determinants for strongly starlike functions, Bol. Soc. Mat. Mex. (3) 27 (2), 1-16, 2021.
  • [22] V. Kumar, S. Kumar and V. Ravichandran, Third Hankel determinant for certain classes of analytic functions, in: International Conference on Recent Advances in Pure and Applied Mathematics, 223-231, Springer, Singapore, 2018.
  • [23] S. Kumar and V. Ravichandran, A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2), 199-212, 2016.
  • [24] O.S. Kwon, A. Lecko and Y.J. Sim, The bound of the Hankel determinant of the third kind for starlike functions, Bull. Malays. Math. Sci. Soc. 42 (2), 767-780, 2019.
  • [25] A. Lecko, Y.J. Sim and B. Śmiarowska, The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1/2, Complex Anal. Oper. Theory 13 (5), 2231-2238, 2019.
  • [26] S.K. Lee, V. Ravichandran and S. Supramaniam, Bounds for the second Hankel de- terminant of certain univalent functions, J. Inequal. Appl. 2013 (1), 1-17, 2013.
  • [27] R.J. Libera and E.J. Złotkiewicz, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (2), 251-257, 1983.
  • [28] W.C. Ma and D. Minda, A unified treatment of some special classes of univalent func- tions, in: Proceedings of the Conference on Complex Analysis, 157-169, International Press Inc., 1992.
  • [29] P.T. Mocanu, Une propriété de convexité généralisée dans la théorie de la représen- tation conforme, Mathematica (Cluj) 34 (11), 127-133, 1969.
  • [30] S. Owa, On the classes of univalent functions with negative coefficients, Math. Japon, 27 (4), 409-416, 1982.
  • [31] Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. London Math. Soc. 41, 111-122, 1966.
  • [32] Ch. Pommerenke, On the Hankel determinants of univalent functions, Mathematika 14, 108-112, 1967.
  • [33] V. Ravichandran and S. Verma, Bound for the fifth coefficient of certain starlike functions, C. R. Math. Acad. Sci. Paris, 353 (6), 505-510, 2015.
  • [34] M.O. Reade, On close-to-convex univalent functions, Michigan Math. J. 3, 59-62, 1955.
  • [35] M.S. Robertson, Certain classes of starlike functions, Michigan Math. J. 32 (2), 135- 140, 1985.
  • [36] W. Rogosinski, Über positive harmonische Entwicklungen und typisch-reelle Poten- zreihen, Math. Z. 35 (1), 93-121, 1932.
  • [37] K. Sharma, N.K. Jain and V. Ravichandran, Starlike functions associated with a cardioid, Afr. Mat. 27 (5-6), 923-939, 2016.
  • [38] J. Sokół, and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. 19, 101-105, 1996.
  • [39] Y. Sun, Z.-G. Wang and A. Rasila, On third Hankel determinants for subclasses of analytic functions and close-to-convex harmonic mappings, Hacett. J. Math. Stat. 48 (6), 1695-1705, 2019.
  • [40] L.A. Wani and A. Swaminathan, Starlike and convex functions associated with a nephroid domain, Bull. Malays. Math. Sci. Soc. 44 (1), 79-104, 2021.
  • [41] L.A. Wani and A. Swaminathan, Radius problems for functions associated with a nephroid domain, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (4), 178, 2020.
  • [42] K. Ye and L.-H. Lim, Every matrix is a product of Toeplitz matrices, Found. Comput. Math. 16, 577-598, 2016.
  • [43] P. Zaprawa, Third Hankel determinants for subclasses of univalent functions, Mediterr. J. Math. 14 (1), 1-10, 2017.

Coefficient inequalities for certain starlike and convex functions

Year 2022, Volume: 51 Issue: 1, 156 - 171, 14.02.2022

Sushil Kumar Kumar , Asena Çetinkaya

https://doi.org/10.15672/hujms.778148
Cited By: 3

Abstract

In this paper, we consider two Ma--Minda-type subclasses of starlike and convex functions associated with the normalized analytic function $\varphi_{Ne}(z)=1+z-z^3/3$ that maps an open unit disk onto the Nephroid shaped bounded domain in the right--half of the complex plane. We investigate convolution and quasi-Hadamard product properties for the functions belonging to such classes. In addition, we compute best possible estimates on third order Hermitian--Toeplitz determinant and non-sharp estimates on certain third order Hankel determinants for the starlike functions associated with the interior region of Nephroid.

Keywords

Starlike functions convex functions Neproid convolution properties quasi-Hadamard product properties Hermitian--Toeplitz and Hankel determinants

References

  • [1] R.M. Ali, Coefficients of the inverse of strongly starlike functions, Bull. Malays. Math. Sci. Soc. 26 (1), 63-71, 2003.
  • [2] M.F. 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.
  • [3] M.K. Aouf, The quasi-Hadamard product of certain analytic functions, Appl. Math. Lett. 21, 1184-1187, 2008.
  • [4] K.O. Babalola, On H3(1) Hankel determinant for some classes of univalent functions, Ineq. Theory and Appl. 6, 1-7, 2010.
  • [5] N. Breaz and R.M. El-Ashwah, Quasi-Hadamard product of some uniformly analytic and p-valent functions with negative coefficients, Carpathian J. Math. 30 (1), 39-45, 2014.
  • [6] T. Bulboacă, M.K. Aouf and R.M. El-Ashwah, Convolution properties for subclasses of meromorphic univalent functions of complex order, Filomat 26 (1), 153-163, 2012.
  • [7] K. Cudna, O.S. Kwon, A. Lecko, Y.J. Sim and B. Śmiarowska, The second and third- order Hermitian Toeplitz determinants for starlike and convex functions of order , Bol. Soc. Mat. Mex. (3) 26 (2), 361-375, 2020.
  • [8] P.L. Duren, Univalent Functions, 259, Springer, New York, 1983.
  • [9] R.M. El-Ashwah, Some convolution and inclusion properties for subclasses of bounded univalent functions of complex order, Thai J. Math. 12 (2), 373-384, 2014.
  • [10] H. Güney, S. İlhan and J. Sokół, An upper bound for third Hankel determinant of starlike functions connected with k-Fibonacci numbers, Bol. Soc. Mat. Mex. (3) 25 (1), 117-129, 2019.
  • [11] W.K. Hayman, On the second Hankel determinant of mean univalent functions, Proc. London Math. Soc. (3) 18, 77-94, 1968.
  • [12] H.M. Hossen, Quasi-Hadamard product of certain p-valent functions, Demonstratio Math. 33 (2), 277-281, 2000.
  • [13] W. Janowski, Some extremal problems for certain families of analytic functions I, Ann. Polon. Math. 28, 297-326, 1973.
  • [14] P. Jastrz¸ebski B. Kowalczyk, Oh S. Kwon, A. Lecko and Y.J. Sim, Hermitian Toeplitz determinants of the second and third-order for classes of close-to-star functions, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (4), 166, 2020.
  • [15] W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1, 169-185, 1952.
  • [16] R. Kargar, A. Ebadian and J. Sokół, On Booth lemniscate and starlike functions, Anal. Math. Phys. 9 (1), 143-154, 2019.
  • [17] B. Kowalczyk, A. Lecko and Y.J. Sim, The sharp bound for the Hankel determinant of the third kind for convex functions, Bull. Aust. Math. Soc. 97 (3), 435-445, 2018.
  • [18] D. Kucerovsky, K. Mousavand and A. Sarraf, On some properties of Toeplitz matrices, Cogent Math. 3, 2016 (Article ID 1154705).
  • [19] V. Kumar, Hadamard product of certain starlike functions II, J. Math. Anal. Appl. 113, 230-234, 1986.
  • [20] V. Kumar, N. E. Cho, V. Ravichandran and H.M. Srivastava, Sharp coefficient bounds for starlike functions associated with the Bell numbers, Math. Slovaca 69 (5), 1053- 1064, 2019.
  • [21] V. Kumar and S. Kumar, Bounds on Hermitian-Toeplitz and Hankel determinants for strongly starlike functions, Bol. Soc. Mat. Mex. (3) 27 (2), 1-16, 2021.
  • [22] V. Kumar, S. Kumar and V. Ravichandran, Third Hankel determinant for certain classes of analytic functions, in: International Conference on Recent Advances in Pure and Applied Mathematics, 223-231, Springer, Singapore, 2018.
  • [23] S. Kumar and V. Ravichandran, A subclass of starlike functions associated with a rational function, Southeast Asian Bull. Math. 40 (2), 199-212, 2016.
  • [24] O.S. Kwon, A. Lecko and Y.J. Sim, The bound of the Hankel determinant of the third kind for starlike functions, Bull. Malays. Math. Sci. Soc. 42 (2), 767-780, 2019.
  • [25] A. Lecko, Y.J. Sim and B. Śmiarowska, The sharp bound of the Hankel determinant of the third kind for starlike functions of order 1/2, Complex Anal. Oper. Theory 13 (5), 2231-2238, 2019.
  • [26] S.K. Lee, V. Ravichandran and S. Supramaniam, Bounds for the second Hankel de- terminant of certain univalent functions, J. Inequal. Appl. 2013 (1), 1-17, 2013.
  • [27] R.J. Libera and E.J. Złotkiewicz, Coefficient bounds for the inverse of a function with derivative in P, Proc. Amer. Math. Soc. 87 (2), 251-257, 1983.
  • [28] W.C. Ma and D. Minda, A unified treatment of some special classes of univalent func- tions, in: Proceedings of the Conference on Complex Analysis, 157-169, International Press Inc., 1992.
  • [29] P.T. Mocanu, Une propriété de convexité généralisée dans la théorie de la représen- tation conforme, Mathematica (Cluj) 34 (11), 127-133, 1969.
  • [30] S. Owa, On the classes of univalent functions with negative coefficients, Math. Japon, 27 (4), 409-416, 1982.
  • [31] Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. London Math. Soc. 41, 111-122, 1966.
  • [32] Ch. Pommerenke, On the Hankel determinants of univalent functions, Mathematika 14, 108-112, 1967.
  • [33] V. Ravichandran and S. Verma, Bound for the fifth coefficient of certain starlike functions, C. R. Math. Acad. Sci. Paris, 353 (6), 505-510, 2015.
  • [34] M.O. Reade, On close-to-convex univalent functions, Michigan Math. J. 3, 59-62, 1955.
  • [35] M.S. Robertson, Certain classes of starlike functions, Michigan Math. J. 32 (2), 135- 140, 1985.
  • [36] W. Rogosinski, Über positive harmonische Entwicklungen und typisch-reelle Poten- zreihen, Math. Z. 35 (1), 93-121, 1932.
  • [37] K. Sharma, N.K. Jain and V. Ravichandran, Starlike functions associated with a cardioid, Afr. Mat. 27 (5-6), 923-939, 2016.
  • [38] J. Sokół, and J. Stankiewicz, Radius of convexity of some subclasses of strongly starlike functions, Zeszyty Nauk. Politech. Rzeszowskiej Mat. 19, 101-105, 1996.
  • [39] Y. Sun, Z.-G. Wang and A. Rasila, On third Hankel determinants for subclasses of analytic functions and close-to-convex harmonic mappings, Hacett. J. Math. Stat. 48 (6), 1695-1705, 2019.
  • [40] L.A. Wani and A. Swaminathan, Starlike and convex functions associated with a nephroid domain, Bull. Malays. Math. Sci. Soc. 44 (1), 79-104, 2021.
  • [41] L.A. Wani and A. Swaminathan, Radius problems for functions associated with a nephroid domain, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114 (4), 178, 2020.
  • [42] K. Ye and L.-H. Lim, Every matrix is a product of Toeplitz matrices, Found. Comput. Math. 16, 577-598, 2016.
  • [43] P. Zaprawa, Third Hankel determinants for subclasses of univalent functions, Mediterr. J. Math. 14 (1), 1-10, 2017.
There are 43 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Mathematics
Authors

Sushil Kumar Kumar 0000-0003-4665-8011

Asena Çetinkaya 0000-0002-8815-5642

Publication Date February 14, 2022
Published in Issue Year 2022 Volume: 51 Issue: 1

Cite

APA Kumar, S. K., & Çetinkaya, A. (2022). Coefficient inequalities for certain starlike and convex functions. Hacettepe Journal of Mathematics and Statistics, 51(1), 156-171. https://doi.org/10.15672/hujms.778148
AMA Kumar SK, Çetinkaya A. Coefficient inequalities for certain starlike and convex functions. Hacettepe Journal of Mathematics and Statistics. February 2022;51(1):156-171. doi:10.15672/hujms.778148
Chicago Kumar, Sushil Kumar, and Asena Çetinkaya. “Coefficient Inequalities for Certain Starlike and Convex Functions”. Hacettepe Journal of Mathematics and Statistics 51, no. 1 (February 2022): 156-71. https://doi.org/10.15672/hujms.778148.
EndNote Kumar SK, Çetinkaya A (February 1, 2022) Coefficient inequalities for certain starlike and convex functions. Hacettepe Journal of Mathematics and Statistics 51 1 156–171.
IEEE S. K. Kumar and A. Çetinkaya, “Coefficient inequalities for certain starlike and convex functions”, Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, pp. 156–171, 2022, doi: 10.15672/hujms.778148.
ISNAD Kumar, Sushil Kumar - Çetinkaya, Asena. “Coefficient Inequalities for Certain Starlike and Convex Functions”. Hacettepe Journal of Mathematics and Statistics 51/1 (February 2022), 156-171. https://doi.org/10.15672/hujms.778148.
JAMA Kumar SK, Çetinkaya A. Coefficient inequalities for certain starlike and convex functions. Hacettepe Journal of Mathematics and Statistics. 2022;51:156–171.
MLA Kumar, Sushil Kumar and Asena Çetinkaya. “Coefficient Inequalities for Certain Starlike and Convex Functions”. Hacettepe Journal of Mathematics and Statistics, vol. 51, no. 1, 2022, pp. 156-71, doi:10.15672/hujms.778148.
Vancouver Kumar SK, Çetinkaya A. Coefficient inequalities for certain starlike and convex functions. Hacettepe Journal of Mathematics and Statistics. 2022;51(1):156-71.

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