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Xu, Shaoyuan, Cheng, Suyu, Aleksic, Suzana. (1396). Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications. نشریه هنرهای کاربردی, 8(2), 335-353. doi: 10.22075/ijnaa.2017.1857.1483
Shaoyuan Xu; Suyu Cheng; Suzana Aleksic. "Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications". نشریه هنرهای کاربردی, 8, 2, 1396, 335-353. doi: 10.22075/ijnaa.2017.1857.1483
Xu, Shaoyuan, Cheng, Suyu, Aleksic, Suzana. (1396). 'Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications', نشریه هنرهای کاربردی, 8(2), pp. 335-353. doi: 10.22075/ijnaa.2017.1857.1483
Xu, Shaoyuan, Cheng, Suyu, Aleksic, Suzana. Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications. نشریه هنرهای کاربردی, 1396; 8(2): 335-353. doi: 10.22075/ijnaa.2017.1857.1483

Fixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications

International Journal of Nonlinear Analysis and Applications
مقاله 47، دوره 8، شماره 2، اسفند 2017، صفحه 335-353    اصل مقاله (429.09 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22075/ijnaa.2017.1857.1483
نویسندگان
Shaoyuan Xu* 1؛ Suyu Cheng2؛ Suzana Aleksic3
1School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
2Library, Hanshan Normal University, Chaozhou, 521041, China
3Department of Mathematics and Informatics, Faculty of Science, University of Kragujevac, Radoja Domanovi'ca 12, 34000 Kragujevac, Serbia
تاریخ دریافت: 19 دی 1395،  تاریخ بازنگری: 14 تیر 1396،  تاریخ پذیرش: 05 شهریور 1396 
چکیده
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.
کلیدواژه‌ها
cone $b$-metric spaces over Banach algebras؛ non-normal cones؛ $c$-sequences؛ generalized quasi-contractions؛ Fixed point theorem
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