in this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear volterra integral equations of the first and second kinds, which avoids from using starting values. an existence and uniqueness theorem is proved and convergence isverified by using an appropriate variety of the gronwall inequality. application of the method is demonstrated for solving the ...

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.

In this paper, we define the almost uniform convergence and the almost everywhere convergence for cone-valued functions with respect to an operator valued measure. We prove the Egoroff theorem for Pvalued functions and operator valued measure θ : R → L(P, Q), where R is a σ-ring of subsets of X≠ ∅, (P, V) is a quasi-full locally convex cone and (Q, W) is a locally ...