In this paper, we introduce a new system of quasi variational inequalities. The projection technique is used to establish the equivalence between this new system of quasi variational inequalities and the fixed point problem. The fixed point formulation enables us to suggest some parallel projection iterative methods for solving the system of quasi variational inequalities. Convergence analysis ...

We study a concept of 1-local retract in quasi-metric spaces. In this article, we generalize further known results about 1-local retract subsets from metric setting to quasi-metric point of view. In particular we show that any commuting family of nonexpansive self-mappings in a nonempty T0-quasi-metric space (X, d) for which Aq(X) is compact and normal has a common fixed point and the common fi...

Abstract. Recently, Aydi et al. [On fixed point results for α-implicit contractions in quasi-metric spaces and consequences, Nonlinear Anal. Model. Control, 21(1):40–56, 2016] proved some fixed point results involving α-implicit contractive conditions in quasi-b-metric spaces. In this paper we extend and improve these results and derive some new fixed point theorems for implicit contractions in...

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...