Fixed point theory for multivalued maps in Fréchet spaces via degree and index theory

2007 ◽  
Vol 27 (2) ◽  
pp. 399 ◽  
Author(s):  
R.P. Agarwal ◽  
D. O'Regan ◽  
Daya Ram Sahu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Index Theory ◽  
Point Theory ◽  
Fréchet Spaces ◽  
Multivalued Maps

scholarly journals FIXED POINT THEORY FOR VARIOUS CLASSES OF INWARD MULTIVALUED MAPS

2009 ◽  
Vol 81 (1) ◽  
pp. 1-15
Author(s):  
RAVI P. AGARWAL ◽  
DONAL O’REGAN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fréchet Spaces ◽  
Multivalued Maps ◽  
Contractive Type ◽  
Weakly Inward

AbstractIn this paper we present new fixed point theorems for inward and weakly inward type maps between Fréchet spaces. We also discuss Kakutani–Mönch and contractive type maps.

scholarly journals Nonnegative solutions of two-point boundary value problems for nonlinear second order integrodifferential equations in Banach spaces

1991 ◽  
Vol 4 (1) ◽  
pp. 47-69 ◽  
Author(s):  
Dajun Guo
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Index Theory ◽  
Point Theory ◽  
Second Order ◽  
Integrodifferential Equations ◽  
Third Order ◽  
Nonnegative Solutions ◽  
Fixed Point Index Theory

In this paper, we combine the fixed point theory, fixed point index theory and cone theory to investigate the nonnegative solutions of two-point BVP for nonlinear second order integrodifferential equations in Banach spaces. As application, we get some results for the third order case. Finally, we give several examples for both infinite and finite systems of ordinary nonlinear integrodifferential equations.

scholarly journals Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

2002 ◽  
Vol 30 (10) ◽  
pp. 627-635 ◽  
Author(s):  
S. L. Singh ◽  
S. N. Mishra
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Multivalued Maps

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

Fixed points of multivalued maps under local Lipschitz conditions and applications

2019 ◽  
Vol 150 (3) ◽  
pp. 1467-1494
Author(s):  
Claudio A. Gallegos ◽  
Hernán R. Henríquez
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theory ◽  
Mild Solutions ◽  
Abstract Cauchy Problem ◽  
Point Theory ◽  
Vector Subspace ◽  
Multivalued Maps ◽  
Lipschitz Continuous

AbstractIn this work we are concerned with the existence of fixed points for multivalued maps defined on Banach spaces. Using the Banach spaces scale concept, we establish the existence of a fixed point of a multivalued map in a vector subspace where the map is only locally Lipschitz continuous. We apply our results to the existence of mild solutions and asymptotically almost periodic solutions of an abstract Cauchy problem governed by a first-order differential inclusion. Our results are obtained by using fixed point theory for the measure of noncompactness.

Sign in / Sign up

Export Citation Format

Share Document