In this paper, we modify the KF-iteration process into hyperbolic metric spaces where symmetry condition is satisfied and establish weak w2-stability data dependence results for contraction mappings. We also prove some Δ-convergence strong convergence theorems generalized (α,β)-nonexpansive type 1 Finally, offer a numerical example of mappings show that more effective than other iterations. Our...

We prove a scaling limit theorem for discrete Galton–Watson processes in varying environments. A simple sufficient condition the weak convergence Skorokhod space is given terms of probability generating functions. The gives rise to continuous-state branching environments studied recently by several authors.

Although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. Some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.Here, after criticizi...

‎In the present paper we investigate the $L_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time Markov processes with general state‎ ‎spaces‎. ‎We provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $L_1$-weak ergodicity‎. ‎Moreover‎, ‎we apply‎ ‎the obtained results to establish $L_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

Several convergence and stability issues of the balanced implicit methods (BIMs) for systems of real-valued ordinary stochastic differential equations are thoroughly discussed. These methods are linear-implicit ones, hence easily implementable and computationally more efficient than commonly known nonlinear-implicit methods. In particular, we relax the so far known convergence condition on its ...

Finite-volume methods for problems involving second-order operators with full diffusion matrix can be used thanks to the definition of a discrete gradient for piecewise constant functions on unstructured meshes satisfying an orthogonality condition. This discrete gradient is shown to satisfy a strong convergence property for the interpolation of regular functions, and a weak one for functions b...

Let E be a real uniformly convex Banach space which has the Fréchet differentiable norm, and K a nonempty, closed, and convex subset of E. Let T : K ® K be an asymptotically -strictly pseudocontractive mapping with a nonempty fixed point set. We prove that (I T) is demiclosed at 0 and obtain a weak convergence theorem of the modified Mann’s algorithm for T under suitable control conditions. Mor...

Abstract. Non-divergence form elliptic equations with discontinuous coefficients do not generally posses a weak formulation, thus presenting an obstacle to their numerical solution by classical finite element methods. We propose a new hp-version discontinuous Galerkin finite element method for a class of these problems that satisfy the Cordès condition. It is shown that the method exhibits a co...

In this work, we introduce Fibonacci– Halpern iterative scheme ( FH scheme) in partial ordered Banach space (POB space) for monotone total asymptotically non-expansive mapping (, MTAN mapping) that defined on weakly compact convex subset. We also discuss the results of weak and strong convergence scheme.
 Throughout compactness condition m-th iterate some natural m is necessary to ensure c...