Fixed Point Theorems for Generalized θ-ϕ-Contractions in G-Metric Spaces

Abstract

We introduce the notion of generalized − contraction and establish some new fixed point theorems for this contraction in the setting of complete -metric spaces. The results presented in the paper improve, extend, and unify some known results. Finally, we give an example to illustrate them.

$θ-ϕ-$contraction on $\left(α,η\right)-$complete rectangular $b-$ metric spaces

“…Zheng et al [16] introduced a new type of contractions called θ − φ-contractions in metric spaces and proved a new fixed point theorems for such mapping. (θ 1 ) is increasing ;…”

“…In this paper, using the idea introduced by Zheng et al [16] we investigate some fixed point results for generalized θ − φ−contraction in the setting of (α, η) −compete b−rectangular metric spaces. The results presented in the paper are improved and extended by Jamshiad [10], Kannan [12] and Reich [14].…”