Abstract

In this paper, we define generalized $\varphi-$quasi contraction map which is more general than strict quadratic quasi contraction map by using an altering distance function $\varphi$ and prove the existence and uniqueness of fixed points of these maps satisfying asymptotically regular property in the setting of complete metric spaces. We extend these results to $T$-orbitally complete metric spaces. Examples are provided to illustrate our results. Our results generalize Theorem 4 of [O. Popescu, G. Stan, \emph{Some fixed point theorems for quadratic quasi contractive mappings}, Symmetry, \textbf{11} (2019)].

Keywords: Fixed point; strict quadratic quasi contraction map; altering distance function; generalized $\varphi-$quasi contraction map; $T$-orbitally complete metric space.

MSC: 47H10, 54H25

DOI: 10.57016/MV-YWCY8220

Pages:  1--12