A random iteration algorithm for graph-directed sets is defined and discussed. Similarly to the Barnsley-Elton’s theorem, it is shown that almost all sequences obtained by this algorithm reflect a probability measure which is invariant with respect to the system of contractions with probabilities.

Many authors have proposed fixed-point algorithms for obtaining a fixed point of G-nonexpansive mappings without using inertial techniques. To improve convergence behavior, some accelerated methods been introduced. The main aim this paper is to use coordinate affine structure create an algorithm with technique countable family in Hilbert space symmetric directed graph G and prove the weak theor...

A random number generator is proposed based on a theorem about existence of chaos in fixed point iteration of xn = cot(xn−1). Digital computer simulation of this function iteration exhibits random behavior. A method is proposed to extract random bytes from this simulation. Diehard and NIST test suite for randomness detection is run on this bytes, and it is found to pass all the tests in the sui...

In this paper, we show strong convergence theorems of modified Ishikawa iteration with errors and modified Halpern iteration with error for relatively nonexpansive mappings in a Banach space. The results extend and improve the corresponding results of Nakajo, Takahashi, Kim, Martinez-Yanes, Xu and some others. Mathematics Subject Classification: 47H09; 47H10

In this paper, we apply the modified variational iteration method for solving the boundary layer problem in unbounded domain. The suggested modification is made by introducing He’s polynomials in the correction functional. The fact that the proposed modified variational iteration method solves nonlinear problems without using Adomian’s polynomials is a clear advantage of this technique over the...

Abstract We show that an invariant measure of a Markov operator is contracting in the Hutchison distance, acting on space Borel probability measures Polish space, depends continuously given operator. In addition, we establish estimate for distance between measures. Some applications to weak limit iterates random-valued functions (in particular, so-called random affine maps, occuring, e.g., perp...

We consider counterexamples in the field of random iteration to two well-known theorems of classical complex dynamics Sullivan’s non-wandering theorem and the classification of periodic Fatou components. Random iteration which was first introduced by Fornaess and Sibony (1991) is a generalization of standard complex dynamics where instead of considering iterates of a fixed rational function, on...

In this paper, applying hybrid projection method, a new modified Ishikawa iteration scheme is presented for finding a common element of the solution set of an equilibrium problem and the set of fixed points of relatively nonexpansive mappings in Banach spaces. A numerical example is given and the numerical behaviour of the sequences generated by this algorithm is compared with several existence...

In this paper, we implemented the Modified Iteration Perturbation Method (MIPM) for approximating the periodic behavior of a tapered beam. This problem is formulated as a nonlinear ordinary differential equation with linear and nonlinear terms. The solution is quickly convergent and does not need complicated calculations. Comparing the results of the MIPM with the exact solution shows that this...