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 - <p style="text-align: justify;">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.&nbsp;</p>