scholarly journals Coupled fixed point theorems in partially ordered cone metric spaces

Filomat ◽  
2011 ◽  
Vol 25 (2) ◽  
pp. 137-149 ◽  
Author(s):  
Hui-Sheng Ding ◽  
Lu Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Monotone Mappings ◽  
Ordered Metric Space ◽  
Cone Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Cone Metric

This paper is concerned with mixed monotone mappings in partially ordered cone metric spaces. We establish several fixed point theorems, which generalize and complement some known results. Especially, even in a partially ordered metric space, our main results are generalizations of the fixed point theorems due to Bhaskar and Lakshmikantham [T. Grana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393].

scholarly journals Some fixed point theorems via partial order relations without the monotone property

2015 ◽  
Vol 31 (3) ◽  
pp. 389-394
Author(s):  
WARUT SAKSIRIKUN ◽  
◽  
NARIN PETROT ◽  
Keyword(s):  
Fixed Point ◽  
Partial Order ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Order Relation ◽  
Monotone Mappings ◽  
Complete Metric Spaces ◽  
Nonlinear Anal ◽  
Monotonic Properties

The main aim of this paper is to consider some fixed point theorems via a partial order relation in complete metric spaces, when the considered mapping may not satisfy the monotonic properties. Furthermore, we also obtain some couple fixed point theorems, which can be viewed as an extension of a result that was presented in [V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 7347–7355].

scholarly journals Coupled Fixed Point Theorems of Single-Valued Mapping forc-Distance in Cone Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Zaid Mohammed Fadail ◽  
Abd Ghafur Bin Ahmad
Keyword(s):  
Fixed Point ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Space ◽  
Cone Metric Spaces ◽  
Cone Metric

A new concept of thec-distance in cone metric space has been introduced recently in 2011. The aim of this paper is to extend and generalize some coupled fixed-point theorems onc-distance in cone metric space. Some examples are given.

scholarly journals Common Coupled Fixed Point Theorems of Single-Valued Mapping forc-Distance in Cone Metric Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-24 ◽  
Author(s):  
Zaid Mohammed Fadail ◽  
Abd Ghafur Bin Ahmad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Coupled Fixed Point ◽  
Cone Metric Spaces ◽  
Common Coupled Fixed Point ◽  
Different Types ◽  
The Common ◽  
Contraction Type ◽  
Cone Metric

The existence and uniqueness of the common coupled fixed point in cone metric spaces have been studied by considering different types of contractive conditions. A new concept of thec-distance in cone metric space has been recently introduced in 2011. Then, coupled fixed point results for contraction-type mappings in ordered cone metric spaces and cone metric spaces have been considered. In this paper, some common coupled fixed point results onc-distance in cone metric spaces are obtained. Some supporting examples are given.

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