Fixed point theorems for singlevalued and multivalued generalized contractions in metric spaces endowed with a graph

2011 ◽  
Vol 18 (2) ◽  
pp. 307-327
Author(s):  
Adriana Nicolae ◽  
Donal O'Regan ◽  
Adrian Petruşel
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Multivalued Contractions

Abstract The purpose of this paper is to present some fixed point results for self-generalized (singlevalued and multivalued) contractions in ordered metric spaces and in metric spaces endowed with a graph. Our theorems generalize and extend some recent results in the literature.

scholarly journals Fixed point theorems for multivalued generalized contractions of rational type in complete metric spaces

2014 ◽  
Vol 23 (1) ◽  
pp. 99-106
Author(s):  
ANCA M. OPREA ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Multivalued Operators ◽  
Multivalued Contractions ◽  
Rational Type

The purpose of this paper is to present some fixed point theorems for multivalued contractions of rational type. We extend the results of I. Cabrera, J. Harjani and K. Sadarangan, A fixed point theorem for contractions of rational type in partially ordered metric spaces, Annali dellUniversita di Ferrara, DOI 10.1007/s11565-013-0176-x, to the case of multivalued operators.

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.

Sign in / Sign up

Export Citation Format

Share Document