scholarly journals On Common Fixed Point of Non-Self Mappings Enjoys The T-Approximate Strict Fixed Point Property On the Boundary of Its Domains

2020 ◽  
Vol 1 (2) ◽  
pp. 1-13
Author(s):  
Farshid Khojasteh ◽  
◽  
Mujahid Abbas ◽  
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Property ◽  
Point Property ◽  
Strict Fixed Point

scholarly journals Jungck theorem for triangular maps and related results

2000 ◽  
Vol 1 (1) ◽  
pp. 83 ◽  
Author(s):  
M. Grinc ◽  
L. Snoha
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Periodic Points ◽  
Fixed Point Property ◽  
Compact Interval ◽  
Invariance Property ◽  
Point Property ◽  
Dimensional Cube ◽  
Triangular Maps

<p>We prove that a continuous triangular map G of the n-dimensional cube I<sup>n</sup> has only fixed points and no other periodic points if and only if G has a common fixed point with every continuous triangular map F that is nontrivially compatible with G. This is an analog of Jungck theorem for maps of a real compact interval. We also discuss possible extensions of Jungck theorem, Jachymski theorem and some related results to more general spaces. In particular, the spaces with the fixed point property and the complete invariance property are considered.</p>

scholarly journals A remark on asymptotic regularity and fixed point property

Filomat ◽  
2019 ◽  
Vol 33 (14) ◽  
pp. 4665-4671
Author(s):  
Ravindra Bisht
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Complete Metric Space ◽  
Fixed Point Property ◽  
Point Property ◽  
Necessary And Sufficient Condition ◽  
Asymptotic Regularity ◽  
The Common ◽  
Necessary And Sufficient ◽  
Commuting Mappings

In this paper, we show that orbital continuity of a pair of non-commuting mappings of a complete metric space is equivalent to fixed point property under the Proinov type condition. Furthermore, we establish a situation in which orbital continuity turns out to be a necessary and sufficient condition for the existence of a common fixed point of a pair of mappings yet the mappings are not necessarily continuous at the common fixed point.

scholarly journals Brush spaces and the fixed point property

2011 ◽  
Vol 158 (8) ◽  
pp. 1085-1089 ◽  
Author(s):  
M.M. Marsh ◽  
J.R. Prajs
Keyword(s):  
Fixed Point ◽  
Fixed Point Property ◽  
Point Property

scholarly journals Towards the fixed point property for superreflexive spaces

2001 ◽  
Vol 64 (3) ◽  
pp. 435-444 ◽  
Author(s):  
Andrzej Wiśnicki
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unit Sphere ◽  
Convex Set ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Geometrical Condition

A Banach space X is said to have property (Sm) if every metrically convex set A ⊂ X which lies on the unit sphere and has diameter not greater than one can be (weakly) separated from zero by a functional. We show that this geometrical condition is closely connected with the fixed point property for nonexpansive mappings in superreflexive spaces.

scholarly journals A product space with the fixed point property

2012 ◽  
Vol 2012 (1) ◽  
Author(s):  
Helga Fetter Nathansky ◽  
Enrique Llorens-Fuster
Keyword(s):  
Fixed Point ◽  
Product Space ◽  
Fixed Point Property ◽  
Point Property
Sign in / Sign up

Export Citation Format

Share Document