N fixed point theorems and N best proximity point theorems for generalized contraction in partially ordered metric spaces

2018 ◽  
Vol 20 (1) ◽  
Author(s):  
Jingling Zhang ◽  
Ravi P. Agarwal ◽  
Nan Jiang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Generalized Contraction ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered

scholarly journals Some tripled coincidence point theorems for almost generalized contractions in ordered metric spaces

2012 ◽  
Vol 44 (3) ◽  
pp. 233-251 ◽  
Author(s):  
Erdal KARAPINAR ◽  
Hassen AYDI ◽  
Zead MUSTAFA
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Tripled Fixed Point ◽  
Partially Ordered Metric Spaces ◽  
Partially Ordered ◽  
Nonlinear Anal ◽  
Contractive Type ◽  
Common Fixed Point Theorems

In this paper, we prove tripledcoincidence and common fixed point theorems for $F: X\times X\times X\to X$ and $g:X\to X$ satisfying almost generalized contractions in partially ordered metric spaces. The presented results generalize the theorem of Berinde and Borcut Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal 74(15) (2011)4889--4897. Also, some examples are presented.

scholarly journals Best Proximity Point Results for Modified --Proximal Rational Contractions

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
N. Hussain ◽  
M. A. Kutbi ◽  
P. Salimi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Best Proximity Point ◽  
Point Theory ◽  
Ordered Metric Spaces ◽  
Partially Ordered Metric Spaces ◽  
New Concepts ◽  
Special Cases ◽  
Banach’S Contraction Principle

We first introduce certain new concepts of --proximal admissible and ---rational proximal contractions of the first and second kinds. Then we establish certain best proximity point theorems for such rational proximal contractions in metric spaces. As an application, we deduce best proximity and fixed point results in partially ordered metric spaces. The presented results generalize and improve various known results from best proximity point theory. Several interesting consequences of our obtained results are presented in the form of new fixed point theorems which contain famous Banach's contraction principle and some of its generalizations as special cases. Moreover, some examples are given to illustrate the usability of the obtained results.

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