A Matching Theorem in GFC-Spaces with Application to Saddle Points

2013 ◽  
Vol 734-737 ◽  
pp. 2867-2870
Author(s):  
Kai Ting Wen ◽  
He Rui Li
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Saddle Point ◽  
Point Theorem ◽  
Saddle Points ◽  
Minimax Inequality ◽  
Saddle Point Theorem ◽  
Matching Theorem

In this paper, a matching theorem for weakly transfer compactly open valued mappings is established in GFC-spaces. As applications, a fixed point theorem, a minimax inequality and a saddle point theorem are obtained in GFC-spaces. Our results unify, improve and generalize some known results in recent reference.

scholarly journals On minimax inequalities on spaces having certain contractible subsets

1993 ◽  
Vol 47 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Sehie Park
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Minimax Theorem ◽  
Saddle Point Theorem ◽  
Minimax Inequalities ◽  
Von Neumann ◽  
Matching Theorem ◽  
Quasi Variational Inequality ◽  
Ky Fan

The concept of a convex space is extended to an H-space; that is, a space having certain family of contractible subsets. For such spaces the KKM type theorems, the Fan-Browder fixed point theorem, the Ky Fan type matching theorem, and minimax inequalities are given. Moreover, applications to a von Neumann-Sion type minimax theorem, a saddle point theorem, a quasi-variational inequality, and a Kakutani type fixed point theorem are obtained.

scholarly journals Solvability and algorithms of generalized nonlinear variational-like inequalities in reflexive Banach spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Haiyan Gao ◽  
Lili Wang ◽  
Liangshi Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Point Theorem ◽  
Existence And Uniqueness ◽  
Minimax Inequality ◽  
Reflexive Banach Spaces ◽  
Uniqueness Of Solutions ◽  
Auxiliary Principle Technique

Abstract This paper deals with solvability and algorithms for a new class of generalized nonlinear variational-like inequalities in reflexive Banach spaces. By employing the Banach’s fixed point theorem, Schauder’s fixed point theorem, and FanKKM theorem, we obtain a sufficient condition which guarantees the existence of solutions for the generalized nonlinear variational-like inequality. We introduce also an auxiliary variational-like inequality and, by utilizing the minimax inequality, get the existence and uniqueness of solutions for the auxiliary variational-like inequality, which is used to suggest an iterative algorithm for solving the generalized nonlinear variational-like inequality. Under certain conditions, by means of the auxiliary principle technique, we both establish the existence and uniqueness of solutions for the generalized nonlinear variational-like inequality and discuss the convergence of iterative sequences generated by the iterative algorithm. Our results extend, improve, and unify several known results in the literature.

Analysis of Solitary Waves in Arteries

2003 ◽  
Author(s):  
G. Nakhaie Jazar ◽  
M. Mahinfalah ◽  
M. Rastgaar Aagaah ◽  
F. Fahimi
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Solitary Wave ◽  
Saddle Point ◽  
Equilibrium Point ◽  
Solitary Waves ◽  
Point Theorem ◽  
Wave Motion ◽  
Straightforward Method ◽  
Nonlinear Character

Solitary waves are coincided with separaterices, which surrounds an equilibrium point with characteristics like a center, a sink, or a source. The existence of closed or spiral orbits in phase plane predicts the existence of such an equilibrium point. If there exists another saddle point near that equilibrium point, separatrix orbit appears. In order to prove the existence of solution for any kind of boundary value problem, we need to apply a fixed-point theorem. We have used the Schauder’s fixed-point theorem to show that there exists at least one nontrivial solution for equation of wave motion in arteries, which has a spiral characteristic. The equation of wave motion in arteries has a nonlinear character. Thus, the amplitude of the wave depends on the wave velocity. There is no general analytical or straightforward method for prediction of the amplitude of the solitary wave. Therefore, it must be found by numerical or nonstraightforward methods. We introduce and analyse three methods: saddle point trajectory, escape moving time, and escape moving energy. We apply these methods and show that the results of them are in agreement, and the amplitude of a solitary wave is predictable.

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion
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