On the Regularization of Projection Methods for Solving Ill-Posed Problems.
On the relationship between difference and projection-difference methods
On the row sum condition and the convergence of iteration processes (Preliminary communication)
On the semilocal convergence of a two-step Newton-like projection method for ill-posed equations
We present new semilocal convergence conditions for a two-step Newton-like projection method of Lavrentiev regularization for solving ill-posed equations in a Hilbert space setting. The new convergence conditions are weaker than in earlier studies. Examples are presented to show that older convergence conditions are not satisfied but the new conditions are satisfied.
On the solution and applications of generalized equations using Newton's method
We provide local and semilocal convergence results for Newton's method when used to solve generalized equations. Using Lipschitz as well as center-Lipschitz conditions on the operators involved instead of just Lipschitz conditions we show that our Newton-Kantorovich hypotheses are weaker than earlier sufficient conditions for the convergence of Newton's method. In the semilocal case we provide finer error bounds and a better information on the location of the solution. In the local case we can provide...
On the solution of a class of equations with monotone operators by iteration and projection-iteration
On the solution of functional equations with linear bounded operators (Preliminary communication)
On the solution of homogeneous functional equations in Hilbert space
On the Stability of Jungck–Mann, Jungck–Krasnoselskij and Jungck Iteration Processes in Arbitrary Banach Spaces
In this paper, we establish some stability results for the Jungck–Mann, Jungck–Krasnoselskij and Jungck iteration processes in arbitrary Banach spaces. These results are proved for a pair of nonselfmappings using the Jungck–Mann, Jungck–Krasnoselskij and Jungck iterations. Our results are generalizations and extensions to a multitude of stability results in literature including those of Imoru and Olatinwo [8], Jungck [10], Berinde [1] and many others.
On the Stability of the Functional Quadratic on A-orthogonal Vectors
On the Stability of the Ritz Procedure for Nonlinear Problems.
On the Steps of Convergence of Approximate Eigenvectors in the Rayleigh-Schrödinger Series.
On the stochastic regularity of sequence transformations operating in a Banach space
On the worst scenario method: Application to a quasilinear elliptic 2D-problem with uncertain coefficients
We apply a theoretical framework for solving a class of worst scenario problems to a problem with a nonlinear partial differential equation. In contrast to the one-dimensional problem investigated by P. Harasim in Appl. Math. 53 (2008), No. 6, 583–598, the two-dimensional problem requires stronger assumptions restricting the admissible set to ensure the monotonicity of the nonlinear operator in the examined state problem, and, as a result, to show the existence and uniqueness of the state solution....
Optimal order yielding discrepancy principle for simplified regularization in Hilbert scales: finite-dimensional realizations.
Optimal radius of convergence of interpolatory iterations for operator equations.
Optimale Approximation linearer Funktionale auf periodischen Funktionen.
Optimale Interpolations- und Approximationssysteme.
Original title unknown
Ostrowski-Kantorovich theorem and -order of convergence of Halley method in Banach spaces
Ostrowski-Kantorovich theorem of Halley method for solving nonlinear operator equations in Banach spaces is presented. The complete expression of an upper bound for the method is given based on the initial information. Also some properties of -order of convergence and sufficient asymptotic error bound will be discussed.