On the New Trends Regarding Nonlinear Contractions

Abstract

The concept of nonlinear contractions is studied by the researchers in the area of Metric Fixed Point Theory more than a half of the century, but during the last decade we are witnessing tremendous interest in the new approach in the area of nonlinear contractions, the concept of F-contraction. This idea has been broadly investigated and there are numerous results regarding modifications of F-contraction and its generalizations in various settings. We will collect several modifications, comment on their mutual relation along with their relation with some other types of nonlinear contractions, and discuss some new result regarding its generalizations. Also, we will present some applications of those fixed point theorems and compare them with previous results regarding those problems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.