Theorem of Existence and Uniqueness of Fixed Points of Monotone Operators

2015 ◽  
pp. 11-17
Author(s):  
Hui Luan ◽  
Zhihong Xia
Keyword(s):  
Fixed Points ◽  
Existence And Uniqueness ◽  
Monotone Operators

scholarly journals Some Fixed Point Results on Rectangular Metric-Like Spaces Endowed with a Graph

Symmetry ◽  
2018 ◽  
Vol 11 (1) ◽  
pp. 18 ◽  
Author(s):  
Nizar Souayah ◽  
Mehdi Mrad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Existence And Uniqueness ◽  
Real Work

The objective of this paper is to establish the existence and uniqueness of fixed points on rectangular metric-like spaces endowed with a graph. We introduce the notion of some generalized G-contractions principle. The usefulness of the considered metric space in real work is highlighted. The obtained results generalize some notes in the literature. Some examples are presented to support the main results.

scholarly journals Some Globally Stable Fixed Points in b-Metric Spaces

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 555 ◽  
Author(s):  
Umar Batsari ◽  
Poom Kumam ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Fixed Points ◽  
Partial Order ◽  
Existence And Uniqueness ◽  
Contraction Mapping ◽  
Metric Spaces ◽  
Continuous Mapping ◽  
Regularity Property ◽  
Contractive Mappings ◽  
Metric Function ◽  
Globally Stable

In this paper, the existence and uniqueness of globally stable fixed points of asymptotically contractive mappings in complete b-metric spaces were studied. Also, we investigated the existence of fixed points under the setting of a continuous mapping. Furthermore, we introduce a contraction mapping that generalizes that of Banach, Kanan, and Chatterjea. Using our new introduced contraction mapping, we establish some results on the existence and uniqueness of fixed points. In obtaining some of our results, we assume that the space is associated with a partial order, and the b-metric function has the regularity property. Our results improve, and generalize some current results in the literature.

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