On the iterative process of solving nonlinear operator equations in PTL-spaces
On the Mann and Ishikawa iteration processes.
On the monotone convergence of implicit Newton-like methods.
On the Newton-Kantorovich theorem and nonlinear finite element methods
Using a weaker version of the Newton-Kantorovich theorem, we provide a discretization result to find finite element solutions of elliptic boundary value problems. Our hypotheses are weaker and under the same computational cost lead to finer estimates on the distances involved and a more precise information on the location of the solution than before.
On the numerical solution of perturbed bifurcation problems.
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 splitting methods and the proximal point algorithm for maximal monotone operators.
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 some fixed point iteration procedures with errors.
Optimal radius of convergence of interpolatory iterations for operator equations.
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.