In this paper, we first prove a weak convergence theorem by Mann’s iteration for a commutative family of positively homogeneous nonexpansive mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove a strong convergence theorem for such a family of the mappings. These results are new even if the mappings are linear and contractive.

The present paper deals with the approximation of Bézier variants of Baskakov-Kantorovich operators V ∗ n,α in the case 0 < α < 1. Pointwise approximation properties of the operators V ∗ n,α are studied. A convergence theorem of this type approximation for locally bounded functions is established. This convergence theorem subsumes the approximation of functions of bounded variation as a special...

Several preconditioners are proposed for improving the convergence rate of the iterative method derived from splitting. In this paper, the comparison theorem of preconditioned iterative method for regular splitting is proved. And the convergence and comparison theorem for any preconditioner are indicated. This comparison theorem indicates the possibility of finding new preconditioner and splitt...

We prove a theorem which generalizes Poisson convergence for sums of independent random variables taking the values 0 and 1 to a type of “Gibbs convergence” for strongly correlated random variables. The theorem is then used to develop a lattice-to-continuum theory for statistical mechanics.

In this paper, by means of the concept of attractive points of a nonlinear mapping, we prove strong convergence theorem of the Ishikawa iteration for an (α, β)−generalized hybrid mapping in a uniformly convex Banach space, and obtain weak convergence theorem of the Ishikawa iteration for such a mapping in a Hilbert space.

Under the new Hölder conditions, we consider the convergence analysis of the inverse-free Jarratt method in Banach space which is used to solve the nonlinear operator equation. We establish a new semilocal convergence theorem for the inverse-free Jarratt method and present an error estimate. Finally, three examples are provided to show the application of the theorem.

In this paper by using the idea of mean convergence, weintroduce an iterative scheme for finding a common element of theset of solutions of an equilibrium problem and the fixed points setof a nonspreading-type mappings in Hilbert space. A strongconvergence theorem of the proposed iterative scheme is establishedunder some control conditions. The main result of this paper extendthe results obtain...

In this paper, An effective and simple numerical method is proposed for solving systems of integral equations using radial basis functions (RBFs). We present an algorithm based on interpolation by radial basis functions including multiquadratics (MQs), using Legendre-Gauss-Lobatto nodes and weights. Also a theorem is proved for convergence of the algorithm. Some numerical examples are presented...

In this paper, we introduce the Denjoy-Pettis integral of set-valued mappings and investigate some properties of the set-valued Denjoy-Pettis integral. Finally we obtain the Dominated Convergence Theorem and Monotone Convergence Theorem for set-valued DenjoyPettis integrable mappings.

In the present paper we introduce a q -analogue of the bivariate Durrmeyer operators. A convergence theorem for these operators is established and the rate of convergence in terms of modulus of continuity is determined. Also, a Voronovskaja type theorem has been investigated for these operators. Mathematics subject classification (2010): 41A10, 41A36.