Volume 33, Issue 2
New Fixed Point Results of Generalized $g$-Quasi-Contractions in Cone $b$-Metric Spaces Over Banach Algebras

Anal. Theory Appl., 33 (2017), pp. 118-133.

Published online: 2017-05

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• 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.

54H25, 47H10

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@Article{ATA-33-118, author = {Xu , S.Cheng , S.Aleksić , S. and Piao , Y.}, title = {New Fixed Point Results of Generalized $g$-Quasi-Contractions in Cone $b$-Metric Spaces Over Banach Algebras}, journal = {Analysis in Theory and Applications}, year = {2017}, volume = {33}, number = {2}, pages = {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.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.2017.v33.n2.3}, url = {http://global-sci.org/intro/article_detail/ata/10040.html} }
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.

S. Xu, S. Cheng, S. Aleksić & Y. Piao. (1970). New Fixed Point Results of Generalized $g$-Quasi-Contractions in Cone $b$-Metric Spaces Over Banach Algebras. Analysis in Theory and Applications. 33 (2). 118-133. doi:10.4208/ata.2017.v33.n2.3
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