The Fixed-Point Index and the Fixed-Point Theorems of 1-Set-Contraction Mappings

1988 ◽  
Vol 104 (4) ◽  
pp. 1163 ◽  
Author(s):  
Li Guozhen
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Point Index ◽  
Contraction Mappings

scholarly journals A-properness and fixed point theorems for dissipative type maps

1999 ◽  
Vol 4 (2) ◽  
pp. 83-100 ◽  
Author(s):  
K. Q. Lan ◽  
J. R. L. Webb
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Duality Mapping ◽  
Uniformly Convex ◽  
Point Index ◽  
Weakly Inward ◽  
Convex Subsets

We obtain newA-properness results for demicontinuous, dissipative type mappings defined only on closed convex subsets of a Banach spaceXwith uniformly convex dual and which satisfy a property called weakly inward. The method relies on a new property of the duality mapping in such spaces. New fixed point results are obtained by utilising a theory of fixed point index.

scholarly journals Fixed point theorems in the study of positive strict set-contractions

2021 ◽  
Vol 40 (6) ◽  
pp. 1569-1586
Author(s):  
Salima Mechrouk
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Index Properties ◽  
Point Index

The author uses fixed point index properties and Inspired by the work in Benmezai and Boucheneb (see Theorem 3.8 in [3]) to prove new fixed point theorems for strict set-contraction defined on a Banach space and leaving invariant a cone.

scholarly journals Fixed point index for composite type maps

2009 ◽  
Vol 3 (2) ◽  
pp. 224-235
Author(s):  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Index Theory ◽  
Point Index ◽  
Composite Type

An index theory is presented for compact absorbing contractive Jc or SJc maps and several new fixed point theorems are given for such maps.

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