On some properties of Banach operators.
On some properties of Banach operators. II.
On some properties of focal points.
On the application of measure of noncompactness to existence theorems
On the common fixed point for commuting Lipschitz functions
On the connectedness of the set of fixed points of a compact operator in the Fréchet space
On the continuous dependence of the fixed points for -contractive-type operators
On the convergence and application of Stirling's method
We provide new sufficient convergence conditions for the local and semilocal convergence of Stirling's method to a locally unique solution of a nonlinear operator equation in a Banach space setting. In contrast to earlier results we do not make use of the basic restrictive assumption in [8] that the norm of the Fréchet derivative of the operator involved is strictly bounded above by 1. The study concludes with a numerical example where our results compare favorably with earlier ones.
On the convergence of Neumann series in Banach space.
Si estende un risultato di N. Suzuki sulla convergenza della serie di Neumann per un operatore compatto in uno spazio di Banach.
On the convergence of the Ishikawa iterates to a common fixed point of two mappings
Let be a convex subset of a complete convex metric space , and and be two selfmappings on . In this paper it is shown that if the sequence of Ishikawa iterations associated with and converges, then its limit point is the common fixed point of and . This result extends and generalizes the corresponding results of Naimpally and Singh [6], Rhoades [7] and Hicks and Kubicek [3].
On the convergence of the Ishikawa iteration in the class of quasi contractive operators.
On the convergence of the three-step iteration process in the class of quasi-contractive operators.
On the Converse of Caristi's Fixed Point Theorem
Let X be a nonempty set of cardinality at most and T be a selfmap of X. Our main theorem says that if each periodic point of T is a fixed point under T, and T has a fixed point, then there exist a metric d on X and a lower semicontinuous map ϕ :X→ ℝ ₊ such that d(x,Tx) ≤ ϕ(x) - ϕ(Tx) for all x∈ X, and (X,d) is separable. Assuming CH (the Continuum Hypothesis), we deduce that (X,d) is compact.
On the covering dimension of the fixed point set of certain multifunctions
We study the covering dimension of the fixed point set of lower semicontinuous multifunctions of which many values can be non-closed or non-convex. An application to variational inequalities is presented.
On the equivalence of Mann and Ishikawa iteration methods.
On the existence and convergence of approximate solutions for equilibrium problems in Banach spaces.
On the existence and uniqueness problems of solutions for set-valued and single-valued nonlinear operator equations in probabilistic normed spaces.
On the existence of a maximal element of multivalued mappings in -spaces.
On the existence of a solution for nonlinear operator equations in Fréchet spaces
On the existence of bounded continuous solution of Hammerstein integral equation