On the class of analytic functions defined by Robertson associated with nephroid domain
DOI:
https://doi.org/10.24193/subbmath.2025.1.01Keywords:
Univalent functions, Starlike functions of order $\gamma$, Starlike function with respect to a boundary point, Coefficient estimatesAbstract
The primary focus of this article is to explore a novel subclass, denoted as \(\mathscr{G}_{\mathcal{N}}\), of analytic functions. These functions exhibit starlike properties concerning a boundary point within a nephroid domain. The author obtains representation theorems, establishes growth and distortion theorems, and investigates various implications related to differential subordination. In addition to the investigation of coefficient estimates, the study also explores specific consequences of differential subordination.References
Agarwal, R.P., Jleli, M., Samet, B., Fixed Point Theory in Metric spaces, Springer, 2018.
Berinde, V., Iterative Approximation of Fixed Points, Springer-Verlag Heidelberg Berlin, 2007.
Berinde, V., Petrusel, A., Rus, I.A., Remarks on the terminology of the mappings in fixed point iterative methods in metric spaces, Fixed Point Theory, 24(2023), No. 2, 525-540.
Filip, A.-D., Fixed Point Theory in Kasahara Spaces, Casa Cartii de S tiint a, Cluj-Napoca, 2015.
Filip, A.-D., Fixed point theorems for nonself generalized contractions on a large Kasahara space, Carpathian J. Math., 38(2022), No. 3, 799-809.
Hardy, G.E., Rogers, T.D., A generalization of a xed point theorem of Reich, Canad. Math. Bull., 16(1973), 201-206.
Karapinar, E., Agarwal, R., Aydi, H., Interpolative Reich-Rus-Ciric type contractions on partial metric spaces, Mathematics, 6(2018) 256.
Khojasteh, F., Abbas, M, Costache, S., Two new types of fixed point theorems in complete metric spaces, Abstr. Appl. Anal., 2014, Art. ID 325840, 5pp.
Kirk, W.A., Sims, B., (eds.), Handbook of Metric Fixed Point Theory, Kluwer, 2001.
Park, S., Almost all about Rus-Hicks-Rhoades maps in quasi-metric spaces, Adv. Theory Nonlinear Anal. Appl., 7(2023), No. 2, 455-472.
Petrussel, A., Rus, I.A., Graphic contraction principle and application, In: Th. Rassias et al. (eds.), Mathematical Analysis and Application, Springer, 2019, 395-416.
Rhoades, B.E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226(1977), 257-290.
Rus, I.A., On common fixed points, Stud. Univ. Babes-Bolyai Math., 18(1973), 31-33.
Rus, I.A., Generalized Contractions and Applications, Cluj Univ. Press, Cluj-Napoca, 2001.
Rus, I.A., Relevant classes of weakly Picard operators, An. Univ. Vest Timisoara, Mat.-Inform., 54(2016), no. 2, 3-19.
Rus, I.A., Some variants of contraction principle, generalizations and applications, Stud. Univ. Babes-Bolyai Math., 61(2016), No. 3, 343-358.
Rus, I.A., Around metric coincidence point theory, Stud. Univ. Babes-Bolyai Math., 68(2023), No. 2, 449-463.
Rus, I.A., Petrusel, A., Petrusel, G., Fixed Point Theory, Cluj Univ. Press, Cluj-Napoca, 2008.
Rus, I.A., Serban, M.-A., Basic problems of the metric fixed point theory, Carpathian J. Math., 29(2013), 239-258.
Tongnoi, B., Saturated versions of some fixed point theorems for generalized contractions, Fixed Point Theory, 21(2020), No. 2, 755-766.
Downloads
Published
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Transfer of copyright agreement: When the article is accepted for publication, the authors and the representative of the coauthors, hereby agree to transfer to Studia Universitatis Babeș-Bolyai Mathematica all rights, including those pertaining to electronic forms and transmissions, under existing copyright laws, except for the following, which the authors specifically retain: the authors can use the material however they want as long as it fits the NC ND terms of the license. The authors have all rights for reuse according to the license.