6533b835fe1ef96bd129fdd2
RESEARCH PRODUCT
Fixed point theory for 1-set contractive and pseudocontractive mappings
Jesús Garcia-falsetOmar Muñiz-pérezsubject
Discrete mathematicsComputational MathematicsNonlinear systemIterative methodApplied MathematicsBanach spaceFixed-point theoremUniquenessFixed pointFixed-point propertyCoincidence pointMathematicsdescription
The purpose of this paper is to study the existence and uniqueness of fixed point for a class of nonlinear mappings defined on a real Banach space, which, among others, contains the class of separate contractive mappings, as well as to see that an important class of 1-set contractions and of pseudocontractions falls into this type of nonlinear mappings. As a particular case, we give an iterative method to approach the fixed point of a nonexpansive mapping. Later on, we establish some fixed point results of Krasnoselskii type for the sum of two nonlinear mappings where one of them is either a 1-set contraction or a pseudocontraction and the another one is completely continuous, which extend or complete previous results. In the last section, we apply such results to study the existence of solutions to a nonlinear integral equation.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2013-02-01 | Applied Mathematics and Computation |