DOI: 10.3390/math14213879 ISSN: 2227-7390
Fixed Point for Some Polynomial Contractions
Doha A. Abulhamil, Saud M. AlsulamiIn this paper, we introduce the notion of Kannan polynomial contraction in the setting of metric spaces and establish the existence and uniqueness of fixed points for this class of mappings. Furthermore, we extend the study to b-metric spaces by investigating polynomial contractions and Kannan polynomial contractions in this generalized framework. Sufficient conditions are provided to guaranty the existence and uniqueness of fixed points in b-metric spaces. The results obtained extend several known fixed point theorems from metric spaces to b-metric spaces. Moreover, we illustrate our results with several examples and applications.