the purpose of this paper is to study the convergence and the almost sure t-stability of the modied sp-type random iterative algorithm in a separable banach spaces. the bochner in-tegrability of andom xed points of this kind of random operators, the convergence and the almost sure t-stability for this kind of generalized asymptotically quasi-nonexpansive random mappings are obtained. our resu...

‎Given a frame of a separable Hilbert space $H$‎, ‎we present some‎ ‎iterative methods for solving an operator equation $Lu=f$‎, ‎where $L$ is a bounded‎, ‎invertible and symmetric‎ ‎operator on $H$‎. ‎We present some algorithms‎ ‎based on the knowledge of frame bounds‎, ‎Chebyshev method and conjugate gradient method‎, ‎in order to give some‎ ‎approximated solutions to the problem‎. ‎Then we i...

In this paper, we present two new one-step iterative methods based on Thiele’s continued fraction for solving nonlinear equations. By applying the truncated Thiele’s continued fraction twice, the iterative methods are obtained respectively. Analysis of convergence shows that the new methods are fourth-order convergent. Numerical tests verifying the theory are given and based on the methods, two...

A new iterative method of Ostrowski’s type for the inclusion of one isolated simple or multiple complex zero of a polynomial is established in circular complex arithmetic. Cubic convergence is proved and computationally verifiable initial condition that guarantees the convergence of this inclusion method is stated. In order to demonstrate convergence behavior of the proposed method, two numeric...

In this paper we consider a fourth order differential equation with nonlinear boundary condition. The existence and uniqueness of a solution is proved. An iterative method for its solution is proposed and the convergence of the method is established. An interesting property of the sequence of iterative solution in dependence of the monotonicity of the function in nonlinear BC is investigated. N...

In this paper, we introduce and study a generalized Yosida approximation operator associated to H(·, ·)-co-accretive operator and discuss some of its properties. Using the concept of graph convergence and resolvent operator, we establish the convergence for generalized Yosida approximation operator. Also, we show an equivalence between graph convergence for H(·, ·)-co-accretive operator and gen...

To determine the maximum likelihood estimate in case of the iterative solution of the likelihood equations we need a convergence criterion. Usually numerically motivated convergence criteria are used; we propose a statistically motivated convergence criterion. Our criterion reduces the number of iterations tremendously. The iterative algorithm to solve the equations is known to be unstable in t...