New Class of Multivalent Functions with Negative Coefficients
Abstract
In the present paper, we define a new class NA(n,p,λ,α,β) of multivalent functions which are holomorphic in the unit disk ∆ ={s∈C∶|s|<1}. A necessary and sufficient condition for functions to be in the class NA(n,p,λ,α,β) is obtained. Also, we get some geometric properties like radii of starlikeness, convexity and close-to-convexity, closure theorems, extreme points, integral means inequalities and integral operators.
References
R. Agarwal, J. Gupta and G. S. Paliwal, Geometric properties and neighborhood results for a subclass of analytic functions defined by convolution, International Bulletin of Mathematical Research 2(4) (2015), 5-15.
M. K. Aouf, A. O. Mostafa and A. A. Hussain, Certain subclass of p-valent starlike and convex uniformaly functions defined by convolution, Int. J. Open Problems Compt. Math. 9(1) (2016), 36-60. https://doi.org/10.12816/0026353
E. S. Aqlan, Some problems connected with geometric function theory, Ph.D. Thesis, Pune University, Pune, 2004.
W. G. Atshan and N. A. J. Al-Ziadi, A new subclass of harmonic univalent functions, J. Al-Qadisiyah Comput. Sci. Math. 9(2) (2017), 26-32. https://doi.org/10.29304/jqcm.2017.9.2.140
W. G. Atshan, On a certain class of multivalent functions defined by Hadamard product, Journal of Asian Scientific Research 3(9) (2013), 891-902.
R. Bharati, R. Parvatham and A. Swaminathan, On subclasses of uniformly convex functions and corresponding class of starlike functions, Tamkang J. Math. 28(1) (1997), 17-32. https://doi.org/10.5556/j.tkjm.28.1997.4330
S. H. Hadi, M. Darus, C. Part and J. R. Lee, Some geometric properties of multivalent functions associated with a new generalized q-Mittag-Leffler function, AIMS Mathematics 7(7) (2022), 11772–11783. https://doi.org/10.3934/math.2022656
S. M. Khaimar and M. More, On a subclass of multivalent β-uniformly starlike and convex functions defined by a linear operator, LAENG Internat. J. Appl. Math. 39(3) (2009), Article ID IJAM_39_06.
A. Y. Lashin, On a certain subclass of starlike functions with negative coefficients, J. Ineq. Pure Appl. Math. 10(2) (2009), 1-8.
J. E. Littlewood, On inequalities in the theory of functions, Proc. London Math. Soc. 23(2) (1925), 481-519. https://doi.org/10.1112/plms/s2-23.1.481
S. Owa, The quasi-Hadamard products of certain analytic functions, in Current Topics in Analytic Function Theory, H. M. Srivastava and S. Owa, (Editors), World Scientific Publishing Company, Singapore, New Jersey, London, and Hong Kong, 1992. https://doi.org/10.1142/9789814355896_0019
G. S. Sălăgean, H. M. Hossen and M. K. Aouf, On certain class of p-valent functions with negative coefficients. II, Studia Univ. Babes-Bolyai 69(1) (2004), 77-85.
H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1975), 109-116. https://doi.org/10.1090/S0002-9939-1975-0369678-0
A. K. Wanas and H. M. Ahsoni, Some geometric properties for a class of analytic functions defined by beta negative binomial distribution series, Earthline Journal of Mathematical Sciences 9(1) (2022), 105-116. https://doi.org/10.34198/ejms.9122.105116
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
