Iterates of multidimensional approximation operators via Perov theorem
AbstractThe starting point is an approximation process consisting of linear and positive operators. The purpose of this note is to…
Fixed point theory
Krasnoselskii type theorems in product Banach spaces and applications to systems of nonlinear transport equations and mixed fractional differential equations
AbstractIn this paper, we use a new technique for the treatment of systems based on the advantage of vector-valued norms…
How many steps still left to x*?
Abstract The high speed of \(x_{k}\rightarrow x^\ast\in{\mathbb R}\) is usually measured using the C-, Q- or R-orders: \begin{equation}\tag{$C$} \lim \frac…
Existence and uniqueness of the solution for an integral equation with supremum
AbstractFollowing the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of…
Stability results and qualitative properties for Mann’s algorithm via admissible perturbations technique
AbstractIn this paper we will present data dependence results for Mann iteration schene related to the fixed point inclusion. The…
On the characterizations of partial metrics and quasimetrics
AbstractWe present the relationship between the notion of partial metric, which has applications in Computer Science, that of quasimetric (which…
Solving inverse problems via hemicontractive maps
AbstractWe prove a “collage” theorem for hemicontractive maps and we use it for inverse problems. A numerical example is given.…
The equivalence between Mann–Ishikawa iterations and multistep iteration
AbstractWe show that the convergence of Mann, Ishikawa iterations are equivalent to the convergence of a multistep iteration, for various…
The Equivalence between T-Stabilities of The Krasnoselskij and The Mann Iterations
Abstract We prove the equivalence between the -stabilities of the Krasnoselskij and the Mann iterations; a consequence is the equivalence…
Data Dependence for Ishikawa Iteration When Dealing with Contractive-Like Operators
Abstract We prove a convergence result and a data dependence for Ishikawa iteration when applied to contraction-like operators. An example…