F. Shakeri and M. Dehghan in [13] presented the variational iteration method for solving the model describing biological species living together. Here we suggest the differential transform (DT) method for finding the numerical solution of this problem. To this end, we give some preliminary results of the DT and by proving some theorems, we show that the DT method can be easily applied to mentio...

We look at iterated power generators si = s e i−1 mod N for a random seed s0 ∈ ZN that in each iteration output a certain amount of bits. We show that heuristically an output of (1− 1 e ) logN most significant bits per iteration allows for efficient recovery of the whole sequence. This means in particular that the Blum-Blum-Shub generator should be used with an output of less than half of the b...

In this article we first discuss the existence and uniqueness of a solution for the coincidence problem: Find p ∈ X such that Tp = Sp, where X is a nonempty set, Y is a complete metric space, and T,S :X → Y are two mappings satisfying a Wardowski type condition of contractivity. Later on, we will state the convergence of the Picard-Juncgk iteration process to the above coincidence problem as we...

This paper studies the behavior under iteration of the maps Tab(x, y) = (Fab(x)−y, x) of the plane R2, in which Fab(x) = ax if x ≥ 0 and bx if x < 0. The orbits under iteration correspond to solutions of the nonlinear difference equation xn+2 = 1/2(a− b)|xn+1|+1/2(a+ b)xn+1−xn. This family of piecewise-linear maps has the parameter space (a, b) ∈ R2. These maps are area-preserving homeomorphism...

In this paper, we first show that the second-order cone linear complementarity problem (SOCLCP) can be solved by finding a positive zero s∗ ∈ R of a particular rational function h(s), and we then propose a Krylov subspace method to reduce h(s) to h (s) as in the model reduction. The zero s∗ of h(s) can be accurately approximated by that of h (s) = 0, which itself can be cast as a small eigenval...

In this work, we first introduce almost contraction mappings for a pair of two in cone metric spaces over Banach algebras (CMSBA). Then, observe that the class such setting contains those many well known mappings. Finally, prove some fixed point theorems, and obtain $(S,T)$-stability results Jungck iterations CMSBA.

We further present a new modification to the quadratically convergent iteration formulae proposed by Mamta et al. [Mamta, V. Kanwar, V.K. Kukreja, S. Singh, On a class of quadratically convergent iteration formulae, Appl. Math. Comput. 166 (2005) 633–637] for solving single variable nonlinear equations. It is proven that the modification converges cubically. Further, a new family with cubic con...