1. CMB Online first
|Measures of Noncompactness in Regular Spaces|
Previous results by the author on the connection between three of measures of non-compactness obtained for $L_p$, are extended to regular spaces of measurable functions. An example of advantage in some cases one of them in comparison with another is given. Geometric characteristics of regular spaces are determined. New theorems for $(k,\beta)$-boundedness of partially additive operators are proved.
Keywords:measure of non-compactness, condensing map, partially additive operator, regular space, ideal space
Categories:47H08, 46E30, 47H99, 47G10
2. CMB 2008 (vol 51 pp. 372)
|Picard's Iterations for Integral Equations of Mixed Hammerstein Type |
A new semilocal convergence result for the Picard method is presented, where the main required condition in the contraction mapping principle is relaxed.
Keywords:nonlinear equations in Banach spaces, successive approximations, semilocal convergence theorem, Picard's iteration, Hammerstein integral equations
Categories:45G10, 47H99, 65J15