scholarly journals Topological degree and atypical bifurcation results for a class of multivalued perturbations of Fredholm maps in Banach spaces

2017 ◽  
Vol 18 (1) ◽  
pp. 85-106 ◽  
Author(s):  
Pierluigi Benevieri ◽  
◽  
Pietro Zecca ◽  
Keyword(s):  
Banach Spaces ◽  
Topological Degree ◽  
Fredholm Maps

Linear Operators in Banach Spaces

2018 ◽  
Author(s):  
D. E. Edmunds ◽  
W. D. Evans
Keyword(s):  
Banach Spaces ◽  
Linear Operators ◽  
Fredholm Maps

Three main themes run through this chapter: compact linear operators, measures of non-compactness, and Fredholm and semi-Fredholm maps. Connections are established between these themes so as to derive important results later in the book.

The Topological Degree of A-Proper Maps

1971 ◽  
Vol 23 (3) ◽  
pp. 403-412 ◽  
Author(s):  
H. Ship Fah Wong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Banach Spaces ◽  
Topological Degree ◽  
Fixed Point Theorems ◽  
Brouwer Degree ◽  
Finite Dimensional ◽  
Essential Idea ◽  
Proper Maps ◽  
Finite Dimensional Case

Recently several fixed-point theorems have been proved for new classes of non-compact maps between Banach spaces. First, Petryshyn [15] generalized the concept of compact and quasi-compact maps when he introduced the P-compact maps and proved a fixed-point theorem for this class of maps. Then in [6], de Figueiredo defined the notion of G-operator to unify his own work on fixed-point theorems and that of Petryshyn. He also proved that the class of G-operators was a fairly large one.We notice the following facts: (i) The essential idea in the above cases is that if certain finite-dimensional “approximations” of the map have fixed points, then the map has a fixed point; (ii) One of the tools used in proving fixed-point theorems in the finite-dimensional case is the Brouwer degree and its generalization to maps of the type Identity + Compact in [8].

The topological degree in ordered Banach spaces

2008 ◽  
Vol 24 (10) ◽  
pp. 1583-1592
Author(s):  
Adrian Duma ◽  
Ileana Duma
Keyword(s):  
Banach Spaces ◽  
Topological Degree ◽  
Ordered Banach Spaces

The G-invariant implicit function theorem in infinite dimensions II

1986 ◽  
Vol 102 (3-4) ◽  
pp. 211-220 ◽  
Author(s):  
E. N. Dancer
Keyword(s):  
Banach Spaces ◽  
Group Action ◽  
Implicit Function Theorem ◽  
Implicit Function ◽  
Infinite Dimensions ◽  
Regularity Theorem ◽  
Fredholm Maps

SynopsisIn this paper, we study the perturbation of zeros of maps of Banach spaces where the maps are invariant under continuous groups of symmetries. In some cases, we allow the perturbed maps partially to break the symmetries. Our results improve earlier results of the author by removing smoothness conditions on the group action. The key new idea is a regularity theorem for the zeros of invariant Fredholm maps.

Some surjectivity results for operators of generalized monotone type via a topological degree

2018 ◽  
Vol 34 (3) ◽  
pp. 333-340
Author(s):  
SUK-JOON HONG ◽  
◽  
IN-SOOK KIM ◽  
Keyword(s):  
Hilbert Space ◽  
Banach Spaces ◽  
Topological Degree ◽  
Degree Theory ◽  
Monotone Operators ◽  
Reflexive Banach Spaces ◽  
Space Case ◽  
Monotone Type

We introduce a topological degree for a class of operators of generalized monotone type in reflexive Banach spaces, based on the recent Berkovits degree. Using the degree theory, we give some surjectivity results for operators of generalized monotone type in reflexive Banach spaces. In the Hilbert space case, this reduces to the celebrated Browder-Minty theorem for monotone operators.

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