Fixed Point and Related Theorems for Set-Valued Mappings

2001 ◽  
pp. 643-690 ◽  
Author(s):  
George Xian-Zhi Yuan
Keyword(s):  
Fixed Point ◽  
Set Valued Mappings

scholarly journals Applications of Fixed Point Theorems to Generalized Saddle Points of Bifunctions on Chain-Complete Posets

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jinlu Li ◽  
Ying Liu ◽  
Hongya Gao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Topological Structure ◽  
Fixed Point Theorems ◽  
Equilibrium Problems ◽  
Saddle Points ◽  
Order Relation ◽  
Partial Order Relation ◽  
Chain Complete ◽  
Set Valued Mappings

We apply the extensions of the Abian-Brown fixed point theorem for set-valued mappings on chain-complete posets to examine the existence of generalized and extended saddle points of bifunctions defined on posets. We also study the generalized and extended equilibrium problems and the solvability of ordered variational inequalities on posets, which are equipped with a partial order relation and have neither an algebraic structure nor a topological structure.

scholarly journals F-Metric, F-Contraction and Common Fixed-Point Theorems with Applications

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 586 ◽  
Author(s):  
Awais Asif ◽  
Muhammad Nazam ◽  
Muhammad Arshad ◽  
Sang Og Kim
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Functional Equations ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
The Third ◽  
Set Valued Mappings ◽  
Common Fixed Point Theorems

In this paper, we noticed that the existence of fixed points of F-contractions, in F -metric space, can be ensured without the third condition (F3) imposed on the Wardowski function F : ( 0 , ∞ ) → R . We obtain fixed points as well as common fixed-point results for Reich-type F-contractions for both single and set-valued mappings in F -metric spaces. To show the usability of our results, we present two examples. Also, an application to functional equations is presented. The application shows the role of fixed-point theorems in dynamic programming, which is widely used in computer programming and optimization. Our results extend and generalize the previous results in the existing literature.

scholarly journals SOME FIXED POINT THEOREMS FOR SET-VALUED MAPPINGS IN UNIFORM SPACES

1999 ◽  
Vol 32 (2) ◽  
Author(s):  
Duran Tiirkoglu ◽  
Orhan Özer ◽  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Uniform Spaces ◽  
Set Valued Mappings

scholarly journals Related fixed points for set-valued mappings on two uniform spaces

2004 ◽  
Vol 2004 (69) ◽  
pp. 3783-3791 ◽  
Author(s):  
Duran Türkoğlu ◽  
Brian Fisher
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Uniform Spaces ◽  
Set Valued Mappings

Some related fixed point theorems for set-valued mappings on two complete and compact uniform spaces are proved.

scholarly journals Common Fixed Point Theorems of Greguš Type (ϕ,ψ)-Weak Contraction for R-Weakly Commuting Mappings in 2-Metric Spaces

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Penumarthy Parvateesam Murthy ◽  
Uma Devi Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Metric Spaces ◽  
Weak Contraction ◽  
Weakly Commuting Mappings ◽  
Set Valued Mappings ◽  
Commuting Maps ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem ◽  
Commuting Mappings

The main purpose of this paper is to establish a common fixed point theorem for set valued mappings in 2-metric spaces by generalizing a theorem of Abd EL-Monsef et al. (2009) and Murthy and Tas (2009) by using (ϕ,ψ)-weak contraction in view of Greguš type condition for set valued mappings using R-weakly commuting maps.

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