%0 Journal Article
%T Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
%J International Journal of Nonlinear Analysis and Applications
%I Semnan University
%Z 2008-6822
%A Xu, Shaoyuan
%A Cheng, Suyu
%A Aleksic, Suzana
%D 2017
%\ 12/01/2017
%V 8
%N 2
%P 335-353
%! Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
%K cone $b$-metric spaces over Banach algebras
%K non-normal cones
%K $c$-sequences
%K generalized quasi-contractions
%K Fixed point theorem
%R 10.22075/ijnaa.2017.1857.1483
%X 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 setting of cone $b$-metric spaces over Banach algebras, where the coefficient $s$ satisfies $s\ge 1$. As consequences, we obtain common fixed point theorems for the generalized $g$-quasi-contractions in the setting of such spaces. The main results generalize, extend and unify several well-known comparable results in the literature. Moreover, we apply our main results to some nonlinear equations, which shows that these results are more general than corresponding ones in the setting of $b$-metric or metric spaces.
%U https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf