New Fixed Point Results of Generalized $g$-Quasi-Contractions in Cone $b$-Metric Spaces Over Banach Algebras
Year: 2017
Author: S. Xu, S. Cheng, S. Aleksić, Y. Piao
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 2 : pp. 118–133
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2017.v33.n2.3
Analysis in Theory and Applications, Vol. 33 (2017), Iss. 2 : pp. 118–133
Published online: 2017-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Cone $b$-metric spaces over Banach algebras non-normal cones $c$-sequences generalized $g$-quasi-contractions fixed point theorems.