$S$-metric space is a relatively new concept in the literature and currently there is much attention being given to the generalization of $S$-metric spaces and fixed point theory in these spaces. Recently, the concept of $S$-Menger spaces was introduced in the literature as a generalization of both $S$-metric spaces and Menger spaces. Combinations of Banach and Kannan type contractions are very much important to find fixed point results and there are very few works on $S$-metric spaces that includes both of these type contractions. In this paper, we present a fixed point result in $S$-Menger spaces that includes both Banach type contractions and Kannan type contractions. We have also deduced some corollaries from our result and provided examples to validate our work.
Keywords and Phrases
$S$-metric space, Menger space, S-Menger space, Cauchy sequence, fixed point, $t$-norm.
A.M.S. subject classiﬁcation
47H10, 54H25, 54E70.