We give an analytic proof for the Hausdorff convergence of the midpoint or derived polygon iteration. We generalize this iteration scheme and prove that the generalization converges to a region of positive area and becomes dense in that region. We speculate on the centroid or derived polyhedron iteration.

In this paper, we propose a new iteration process to approximate minimizers of proper convex and lower semi-continuous functions and fixed points of λ-hybrid multivalued mappings in Hilbert spaces. We also provide an example to illustrate the convergence behavior of the proposed iteration process and numerically compare the convergence of the proposed iteration scheme with the existing schemes.

In this paper,we establish fixed points theorems in Banach space using Mann Iteration for nonexpansive and asymtotically nonexpansive mappings . Iteration scheme is defined by (2.1) and (2.2). We extended the work of Mann.

The paper gives the numerical stencil for the two-dimensional convection diffusion equation and the technique of elimination, and builds up the new iterative scheme to solve the implicit difference equation. The scheme’s convergence and its higher rate of convergence than the Jacobi iteration are proved. And the numerical example indicates that the new scheme has the same parallelism and a high...

Let T be a local strongly pseudocontractive and uniformly continuous operator from an arbitrary Banach space X into itself. Under certain conditions, we establish that the Noor iteration scheme with errors both converges strongly to a unique fixed point of T and is almost T -stable. The related results deal with the convergence and almost stability of the Noor iteration scheme with errors of so...

*Correspondence: [email protected] Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai, 50200, Thailand Abstract We prove a convergence theorem of the Mann iteration scheme for a uniformly L-Lipschitzian asymptotically demicontractive mapping in a CAT(κ ) space with κ > 0. We also obtain a convergence theorem of the Ishikawa iteration scheme for a uniformly L-Lipsc...

Let E be a real Banach space, {Ti}i=1 be a finite family of continuous pseudocontractive self mappings of E and G : E → E be a mapping which is both δ -strongly accretive and λ -strictly pseudocontractive of Browder-Petryshyn type such that δ + λ 1 . We propose a new implicit iteration scheme with perturbed mapping G for the approximation of common fixed points of {Ti}i=1 . For an arbitrary ini...

By making use of duality mappings and the Bregman distance, we propose a regularizing Levenberg-Marquardt scheme to solve nonlinear inverse problems in Banach spaces, which is an extension of the one proposed in [6] in Hilbert space setting. The method consists of two components: an outer Newton iteration and an inner scheme. The inner scheme involves a family of convex minimization problems in...

Abstract In this work, we analyze a strategy for solving symmetric algebraic Riccati equation based on the use of efficient high-order iterative scheme. This scheme is more than Newton’s method. Then, propose two two-stage predictor–corrector schemes using an with good accessibility as predictor iteration and corrector iteration. The constructed turn out to be competitive compared commonly used...

Abstract. The shortest paths tree problem consists in finding a spanning tree rooted at a given node, in a directed weighted graph, such that for each node i , the path of the tree which goes from i to the root has minimal weight. We propose an algorithm which is a deterministic version of Howard’s policy iteration scheme. We show that policy iteration is faster than the Bellman (or value itera...