COEFFICIENT INEQUALITIES OF BAZILEVIC FUNCTIONS COLLIGATED WITH CONIC DOMAIN
Keywords:
k-uniformly convex functions, k-uniformly starlike functions, Analytic functions, Janowski function, Bazilevic function, Conic domain, Salagean derivative operator
Abstract
In this paper, the concept of Bazilevic function as well as Janowski function and the conic regions are combined eectively to dene a new domain that exemplify the conic-type regions. The sub-classes of these types of functions which map the open unit disk U onto this changed Conic domain are dened. Also, the sub-classes of k -uniformly Janowski convex and k- uniformly Janowski starlike function involving Bazilevic functions are dened using Salagean derivative operator. New results were obtained along with some corollaries and the consequences of our results were pointed out.
References
[1] H.A. Al - Kharsani and A. Sofo. Subordination results on harmonic k-uniformly convex mappings and related classes. Comput. Math., Appl. 59 (12) (2010) 3718 -3726
[2] A.W.Goodman. Univalent Functions. vol.,I - II, Mariner Publishing Company, Tempa, Florida, USA, 1983.
[3] J. O. Hamzat. Estimates of second and third Hankel determinants for Bazilevic function of order gamma. Unilag J. Math and Appl., 3(2023), 102-112.
[4] J. O. Hamzat. Some properties of a new subclass of m-fold symmetric bi-Bazilevic functions associated with modified sigmoid function. Tbilisi Math. J. 4(1), 2021, 107-118.
[5] J. O. Hamzat. Subordination results associated with generalized Bessel function. J. Nepal Math. Soc. (JNMS), 2(1), 2019, 57-64.
[6] J. O. Hamzat. Coefficient inequalities for bounded turning functions associated with conic domains. EJMAA, 7(2), 2019, 73-78.
[7] J. O. Hamzat and M. T. Raji. Coefficient problem concerning some new subclasses of analytic and univalent functions. J. Frac. Calc. Appl., 11(1), 2020, 91-96.
[8] J. O.Hamzat and O. Fagbemiro. Some properties of a new subclass of Bazilevic functions defined by Catas et al diffierential operator. FUW trends in Science and Technology Journal, 2018, Vol. 3, No. 28, pp. 909 - 917.
[9] J. O. Hamzat and D. O. Makinde. Coefficient bounds for Bazilevic functions involving logistic sigmoid function associated with conic domains. Int. J. Math. Anal. Opt. : Theory and Applications, 2, 2018, 392-400.
[10] W. Janowski. Some extremal problems for certain families of analytic functions. Ann, Polon Math. 28 (1973) 297 -326.
[11] S. Kanas. Coecient estimates in subclass of the Caratheodory class related to conical domains. Acta Math, Univ. Comenian. 74 (2) (2005) 149 - 161.
[12] S. Kanas and A. Wisniowkwa. Conic domains and starlike functions. Rev. Roumaine Math. Pures Appl. 45 (2000) 647 - 657.
[13] S. Kanas, A.Wisniowkwa. Conic regions and k- uniform convexity. J. Comput. Appl. Math. 105 (1999) 327 - 336.
[14] K.I. Noor. On a generalization of uniformly convex and related functions. Comput. Math. Appl. 61 (1) (2011) 117 - 125.
[15] K.I. Noor. Applications of certain operators to the classes related with generalized Janowski functions. Integral Transforms Spec, Funct. 21 (8) (2010).
[16] K.I. Noor,M. Arif and W. UI - Hag. On K- uniformly close - to - convex functions of complex order. Appl. Math. Comput. 215 (2) (2009) 629 - 635.
[17] K. I. Noor and S. N. Malik. On coefficient inequalities of functions associated with conic domains. Computers and Mathematics with Applications 62 (2011), 2209 - 2217.
[18] K.I. Noor, S.N. Malik, M. Arif and M. Raza. On bounded boundary and bounded radius rotation related with Janowski function. World Appl. Sci. J. 12 (6) (2011) 895 - 902.
[19] A. T. Oladipo. Some properties of a subclass of univalent functions, Advance Mathematical Analysis. 4 (1 (2005)), 87 - 93.
[20] A. T.Oladipo and D. Breaz. A brief study of certain class of harmonic functions of Bazilevic Type. ISRN Math. Anal. Article ID179856, 11 pages.
[21] A. T. Oladipo and O. Fagbemiro. Certain class of univalent function with negative coefficients. Indian Journal of Mathematics, Vol., 53, No. 3, 429 - 458.
[22] H. Orhana, E. Deniz and D. Raducanab. The Fekete - Szego problem for subclasses of analytic functions defined by a diffierential operator related to conic domains. Comput. Math. Appl. 59 (1) (2010) 288 - 295.
[23] S. Owa, Y. Polatoglu and E. Yavuz. Coefficient inequalities for classes of uniformly starlike and convex functions. J. Inequal. Pure Appl. Math. 7 (5) (2006) Art. 160.
[24] W. Rogosinski. On the coefficients of subordinate functions. Proc. Lond. Math Soc. 48 (1943) 48 - 82.
[25] H. Selverman. Univalent functions with negative coefficients. Proc. Amer. Math. Soc. 51 (1975) 109 116.
[26] S. Shams, S.R. Kulkarni and J. M. Jahangiri. Classes of uniformly starlike and convex functions. Int. J. Math. Sci. 55 (2004) 2959 2961.
[27] J. Sokol, Classes of multivalent functions associated with a convolution operator. Comput. Math. Appl. 60 (5) (2010) 1343 - 1350.
[2] A.W.Goodman. Univalent Functions. vol.,I - II, Mariner Publishing Company, Tempa, Florida, USA, 1983.
[3] J. O. Hamzat. Estimates of second and third Hankel determinants for Bazilevic function of order gamma. Unilag J. Math and Appl., 3(2023), 102-112.
[4] J. O. Hamzat. Some properties of a new subclass of m-fold symmetric bi-Bazilevic functions associated with modified sigmoid function. Tbilisi Math. J. 4(1), 2021, 107-118.
[5] J. O. Hamzat. Subordination results associated with generalized Bessel function. J. Nepal Math. Soc. (JNMS), 2(1), 2019, 57-64.
[6] J. O. Hamzat. Coefficient inequalities for bounded turning functions associated with conic domains. EJMAA, 7(2), 2019, 73-78.
[7] J. O. Hamzat and M. T. Raji. Coefficient problem concerning some new subclasses of analytic and univalent functions. J. Frac. Calc. Appl., 11(1), 2020, 91-96.
[8] J. O.Hamzat and O. Fagbemiro. Some properties of a new subclass of Bazilevic functions defined by Catas et al diffierential operator. FUW trends in Science and Technology Journal, 2018, Vol. 3, No. 28, pp. 909 - 917.
[9] J. O. Hamzat and D. O. Makinde. Coefficient bounds for Bazilevic functions involving logistic sigmoid function associated with conic domains. Int. J. Math. Anal. Opt. : Theory and Applications, 2, 2018, 392-400.
[10] W. Janowski. Some extremal problems for certain families of analytic functions. Ann, Polon Math. 28 (1973) 297 -326.
[11] S. Kanas. Coecient estimates in subclass of the Caratheodory class related to conical domains. Acta Math, Univ. Comenian. 74 (2) (2005) 149 - 161.
[12] S. Kanas and A. Wisniowkwa. Conic domains and starlike functions. Rev. Roumaine Math. Pures Appl. 45 (2000) 647 - 657.
[13] S. Kanas, A.Wisniowkwa. Conic regions and k- uniform convexity. J. Comput. Appl. Math. 105 (1999) 327 - 336.
[14] K.I. Noor. On a generalization of uniformly convex and related functions. Comput. Math. Appl. 61 (1) (2011) 117 - 125.
[15] K.I. Noor. Applications of certain operators to the classes related with generalized Janowski functions. Integral Transforms Spec, Funct. 21 (8) (2010).
[16] K.I. Noor,M. Arif and W. UI - Hag. On K- uniformly close - to - convex functions of complex order. Appl. Math. Comput. 215 (2) (2009) 629 - 635.
[17] K. I. Noor and S. N. Malik. On coefficient inequalities of functions associated with conic domains. Computers and Mathematics with Applications 62 (2011), 2209 - 2217.
[18] K.I. Noor, S.N. Malik, M. Arif and M. Raza. On bounded boundary and bounded radius rotation related with Janowski function. World Appl. Sci. J. 12 (6) (2011) 895 - 902.
[19] A. T. Oladipo. Some properties of a subclass of univalent functions, Advance Mathematical Analysis. 4 (1 (2005)), 87 - 93.
[20] A. T.Oladipo and D. Breaz. A brief study of certain class of harmonic functions of Bazilevic Type. ISRN Math. Anal. Article ID179856, 11 pages.
[21] A. T. Oladipo and O. Fagbemiro. Certain class of univalent function with negative coefficients. Indian Journal of Mathematics, Vol., 53, No. 3, 429 - 458.
[22] H. Orhana, E. Deniz and D. Raducanab. The Fekete - Szego problem for subclasses of analytic functions defined by a diffierential operator related to conic domains. Comput. Math. Appl. 59 (1) (2010) 288 - 295.
[23] S. Owa, Y. Polatoglu and E. Yavuz. Coefficient inequalities for classes of uniformly starlike and convex functions. J. Inequal. Pure Appl. Math. 7 (5) (2006) Art. 160.
[24] W. Rogosinski. On the coefficients of subordinate functions. Proc. Lond. Math Soc. 48 (1943) 48 - 82.
[25] H. Selverman. Univalent functions with negative coefficients. Proc. Amer. Math. Soc. 51 (1975) 109 116.
[26] S. Shams, S.R. Kulkarni and J. M. Jahangiri. Classes of uniformly starlike and convex functions. Int. J. Math. Sci. 55 (2004) 2959 2961.
[27] J. Sokol, Classes of multivalent functions associated with a convolution operator. Comput. Math. Appl. 60 (5) (2010) 1343 - 1350.
Published
2024-11-30
How to Cite
FAGBEMIRO, O. (2024). COEFFICIENT INEQUALITIES OF BAZILEVIC FUNCTIONS COLLIGATED WITH CONIC DOMAIN. Unilag Journal of Mathematics and Applications, 4(1), 35-50. Retrieved from http://lagjma.unilag.edu.ng/article/view/2282
Section
Articles
Copyright (c) 2024 OLALEKAN FAGBEMIRO
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