6533b82efe1ef96bd12932d3

RESEARCH PRODUCT

Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness

Elena Moreno-galvezJesús Garcia-falsetKhalid LatrachMohamed-aziz Taoudi

subject

Discrete mathematicsQuantitative Biology::Neurons and CognitionPicard–Lindelöf theoremApplied MathematicsFixed-point theoremFixed-point propertyKrasnoselskii fixed point theoremSchauder fixed point theoremNonlinear integral equationsMeasure of weak noncompactnessBrouwer fixed-point theoremKakutani fixed-point theoremContraction (operator theory)Nonlinear operatorsAnalysisMathematics

description

Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.

yearjournalcountryeditionlanguage
2012-03-01Journal of Differential Equations
10.1016/j.jde.2011.11.012http://dx.doi.org/10.1016/j.jde.2011.11.012