scholarly journals Fixed Point Theorems of Set-Valued Mappings in Partially Ordered Hausdorff Topological Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shujun Jiang ◽  
Zhilong Li ◽  
Shihua Luo
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Monotone Mappings ◽  
Topological Spaces ◽  
Partially Ordered ◽  
Set Valued Mappings

In this work, several fixed point theorems of set-valued monotone mappings and set-valued Caristi-type mappings are proved in partially ordered Hausdorff topological spaces, which indeed extend and improve many recent results in the setting of metric spaces.

scholarly journals Tripled fixed point theorems for monotone mappings in partially ordered metric spaces

2012 ◽  
Vol 28 (2) ◽  
pp. 215-222
Author(s):  
MARIN BORCUT ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Monotone Mappings ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Partially Ordered ◽  
Contractive Type

In this paper, we introduce the concept of tripled fixed point for nonlinear and monotone mappings in partially ordered complete metric spaces and obtain existence as well as existence and uniqueness theorems for contractive type mappings. Our results generalize and extend recent tripled fixed point theorems established by Berinde and Borcut [Berinde, V., Borcut, M., Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces. Nonlinear Anal. 74 (2011) 4889–4897]. Examples to support our new results are given.

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].

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