Fixed points of almost generalized weakly contractive maps with rational expressions in $S$-metric spaces

G. V. R. Babu 1 , P. D. Sailaja 2 * and G. Srichandana 3

doi:10.26637/MJM0802/0047

Fixed points of almost generalized weakly contractive maps with rational expressions in $S$-metric spaces

Authors :

G. V. R. Babu ¹ , P. D. Sailaja ^{2 *} and G. Srichandana ³

Author Address :

1^,3 Department of Mathematics, Andhra University, Visakhapatnam-530003, India.
² Department of Mathematics, Lendi Institute of Engineering and Technology, Vizianagaram-535005, India.
³ Department of Mathematics, Satya Institute of Technology and Management, Vizianagaram-535002, India.

*Corresponding author.

Abstract :

In this paper, we prove the existence and uniqueness of fixed points of $(\varphi, \psi)$-almost generalized weakly contractive maps with rational expressions in S-metric spaces. Also, we prove the existence and uniqueness of fixed points of $\alpha$-admissible almost weak $\psi$-contraction maps with rational expressions in $S$-metric spaces. Our results extend the results of Jaggi \cite{Jaggi} , Dass and Gupta \cite{Dass} to $S$-metric spaces. Also our results extend and generalize the results of Sedghi, Shobe and Aliouche \cite{Sedghi0}. Supporting examples are provided to our results.

Keywords :

$S$-metric space, fixed point, almost generalized weakly contractive maps, $\alpha$-admissible maps.

DOI :

10.26637/MJM0802/0047

Article Info :

Received : December 21, 2019; Accepted : April 13, 2020.