Search results for "fixed point theory"
showing 7 items of 7 documents
Normal forms of hyperbolic logarithmic transseries
2021
We find the normal forms of hyperbolic logarithmic transseries with respect to parabolic logarithmic normalizing changes of variables. We provide a necessary and sufficient condition on such transseries for the normal form to be linear. The normalizing transformations are obtained via fixed point theorems, and are given algorithmically, as limits of Picard sequences in appropriate topologies.
On the structure of the set of equivalent norms on ℓ1 with the fixed point property
2012
Abstract Let A be the set of all equivalent norms on l 1 which satisfy the FPP. We prove that A contains rays. In fact, every renorming in l 1 which verifies condition (⁎) in Theorem 2.1 is the starting point of a (closed or open) ray composed by equivalent norms on l 1 with the FPP. The standard norm ‖ ⋅ ‖ 1 or P.K. Linʼs norm defined in Lin (2008) [12] are examples of such norms. Moreover, we study some topological properties of the set A with respect to some equivalent metrics defined on the set of all norms on l 1 equivalent to ‖ ⋅ ‖ 1 .
An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations
2020
In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.
On Ekeland's variational principle in partial metric spaces
2015
In this paper, lower semi-continuous functions are used to extend Ekeland's variational principle to the class of parti al metric spaces. As consequences of our results, we obtain some fixed p oint theorems of Caristi and Clarke types.
MR3269340 Reviewed O'Regan, Donal Lefschetz type theorems for a class of noncompact mappings. J. Nonlinear Sci. Appl. 7 (2014), no. 5, 288–295. (Revi…
2015
Lefschetz fixed-point theorem furnishes a way for counting the fixed points of a suitable mapping. In particular, the Lefschetz fixed-point theorem states that if Lefschetz number is not zero, then the involved mapping has at least one fixed point, that is, there exists a point that does not change upon application of mapping. ewline Let $f={f_q}:E o E$ be an endomorphism of degree zero of graded vector space $E={E_q}$. Let $ ilde{E}=E setminus {x in E : f^n(x)=0, mbox{ for some }n in mathbb{N}}$. Define the generalized Lefschetz number $Lambda(f)$ by $$Lambda(f)=sum_{q geq 0}(-1)^qmbox{Tr}(f_q),$$ where $mbox{Tr}(f)=mbox{tr}( ilde{f})$ is the generalized trace of $f$, ``tr'' is the ordinar…
Recensione: MR3038069 Reviewed Banaś, Józef; Ben Amar, Afif Measures of noncompactness in locally convex spaces and fixed point theory for the sum of…
2013
About Applications of the Fixed Point Theory
2017
AbstractThe fixed point theory is essential to various theoretical and applied fields, such as variational and linear inequalities, the approximation theory, nonlinear analysis, integral and differential equations and inclusions, the dynamic systems theory, mathematics of fractals, mathematical economics (game theory, equilibrium problems, and optimisation problems) and mathematical modelling. This paper presents a few benchmarks regarding the applications of the fixed point theory. This paper also debates if the results of the fixed point theory can be applied to the mathematical modelling of quality.