TY - JOUR
ID - 2787
TI - Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
JO - International Journal of Nonlinear Analysis and Applications
JA - IJNAA
LA - en
SN - 2008-6822
AU - Xu, Shaoyuan
AU - Cheng, Suyu
AU - Aleksic, Suzana
AD - School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
AD - Library, Hanshan Normal University, Chaozhou, 521041, China
AD - Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi'ca 12, 34000 Kragujevac, Serbia
Y1 - 2017
PY - 2017
VL - 8
IS - 2
SP - 335
EP - 353
KW - cone $b$-metric spaces over Banach algebras
KW - non-normal cones
KW - $c$-sequences
KW - generalized quasi-contractions
KW - Fixed point theorem
DO - 10.22075/ijnaa.2017.1857.1483
N2 - 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.
UR - https://ijnaa.semnan.ac.ir/article_2787.html
L1 - https://ijnaa.semnan.ac.ir/article_2787_c82fdf395409faa23840674b2855da21.pdf
ER -