Fixed Point and Convergence Results for Nonexpansive 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.

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Fixed point theorems of mean nonexpansive set-valued mappings in Banach spaces

Journal of Fixed Point Theory and Applications ◽

10.1007/s11784-017-0401-9 ◽

2017 ◽

Vol 19 (3) ◽

pp. 2129-2143 ◽

Cited By ~ 8

Author(s):

Lili Chen ◽

Lu Gao ◽

Deyun Chen

Keyword(s):

Fixed Point ◽

Banach Spaces ◽

Fixed Point Theorems ◽

Set Valued Mappings

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Verification of Iterative Methods for the Linear Complementarity Problem

Handbook of Research on Modern Optimization Algorithms and Applications in Engineering and Economics - Advances in Computational Intelligence and Robotics ◽

10.4018/978-1-4666-9644-0.ch021 ◽

2016 ◽

pp. 545-580 ◽

Cited By ~ 2

Author(s):

H. Saberi Najafi ◽

S. A. Edalatpanah

Keyword(s):

Fixed Point ◽

Iterative Methods ◽

Linear Complementarity Problem ◽

Numerical Experiments ◽

Linear Complementarity Problems ◽

Linear Complementarity ◽

Convergence Results ◽

Fixed Point Principle ◽

Preconditioned Iterative ◽

Preconditioned Iterative Methods

In the present chapter, we give an overview of iterative methods for linear complementarity problems (abbreviated as LCPs). We also introduce these iterative methods for the problems based on fixed-point principle. Next, we present some new properties of preconditioned iterative methods for solving the LCPs. Convergence results of the sequence generated by these methods and also the comparison analysis between classic Gauss-Seidel method and preconditioned Gauss-Seidel (PGS) method for LCPs are established under certain conditions. Finally, the efficiency of these methods is demonstrated by numerical experiments. These results show that the mentioned models are effective in actual implementation and competitive with each other.

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

Mathematics ◽

10.3390/math7070586 ◽

2019 ◽

Vol 7 (7) ◽

pp. 586 ◽

Cited By ~ 3

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.

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