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 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 The fixed point index for accretive mapping withK—set contraction perturbation in cones

1996 ◽  
Vol 19 (2) ◽  
pp. 287-290 ◽  
Author(s):  
Yu-Qing Chen
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Index ◽  
Fixed Point Theorems ◽  
Accretive Mapping ◽  
Point Index

LetPbe cone Banach spaceE,A,Kare two mappings inP,Aaccretive,KisK—set contraction, then fixed point index defined for mapping−A+K, some fixed point theorems are also deduced.

scholarly journals A Generalization of Mahadevan's Version of the Krein-Rutman Theorem and Applications top-Laplacian Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Yujun Cui ◽  
Jingxian Sun
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Boundary Value Problems ◽  
Fixed Point Index ◽  
Boundary Value ◽  
Point Index ◽  
Homogeneous Operator ◽  
Existence Of Positive Solutions ◽  
Positive Eigenfunction ◽  
Homogeneous Operators

We will present a generalization of Mahadevan’s version of the Krein-Rutman theorem for a compact, positively 1-homogeneous operator on a Banach space having the properties of being increasing with respect to a conePand such that there is a nonzerou∈P∖{θ}−Pfor whichMTpu≥ufor some positive constantMand some positive integerp. Moreover, we give some new results on the uniqueness of positive eigenvalue with positive eigenfunction and computation of the fixed point index. As applications, the existence of positive solutions forp-Laplacian boundary-value problems is considered under some conditions concerning the positive eigenvalues corresponding to the relevant positively 1-homogeneous operators.

scholarly journals Fixed point index approach for solutions of variational inequalities

2005 ◽  
Vol 2005 (12) ◽  
pp. 1879-1887 ◽  
Author(s):  
Yisheng Lai ◽  
Yuanguo Zhu ◽  
Yinbing Deng
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Point Index ◽  
Reflexive Banach Space ◽  
The Other ◽  
Multivalued Mappings ◽  
Point Index ◽  
Upper Semicontinuous ◽  
Index Approach

By using fixed point index approach for multivalued mappings, the existence of nonzero solutions for a class of generalized variational inequalities is studied in reflexive Banach space. One of the mappings concerned here is coercive or monotone and the other is set-contractive or upper semicontinuous.

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