TY - JOUR T1 - New Fixed Point Results of Generalized $g$-Quasi-Contractions in Cone $b$-Metric Spaces Over Banach Algebras AU - Xu , S. AU - Cheng , S. AU - Aleksić , S. AU - Piao , Y. JO - Analysis in Theory and Applications VL - 2 SP - 118 EP - 133 PY - 2017 DA - 2017/05 SN - 33 DO - http://doi.org/10.4208/ata.2017.v33.n2.3 UR - https://global-sci.org/intro/article_detail/ata/10040.html KW - Cone $b$-metric spaces over Banach algebras, non-normal cones, $c$-sequences, generalized $g$-quasi-contractions, fixed point theorems. AB -

In this paper, we introduce the concept of generalized $g$-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 $g$-quasi-contractions with the spectral radius $r(\lambda)$ of the $g$-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 $s\ge 1$. The main results generalize, extend and unify several well-known comparable results in the literature.