In this paper, we prove the weak convergence of a modified Khan iteration for nonself I nonexpansive mapping in a Banach space which satisfies Opial’s condition. Our result extends and improves these announced by S. Chornphrom and S.Phonin [Weak Converges Theorem of Noor iterative Scheme for Nonself I-Nonexpansive mapping, Thai Journal of Mathematics Volume 7(2009) no.2:311-317].

We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E. Keywords—Common fixed point, Mann iteration, Multivalued mapping, weak convergence.

In this paper we present existence theorems for the second order discrete boundary value problem in Banach spaces under weaker conditions we have known. We suppose the weak sequential continuity and some conditions expressed in terms of the measure of weak noncompactness.

Let E and F be Banach spaces. We say that E is F -saturated if every infinite dimensional closed subspace of E contains an isomorphic copy of F . In [2], it is shown that there exists a c0-saturated Banach space with an unconditional basis whose dual contains an isomorphic copy of l2. In this note, we give an example where the dual situation occurs. It is shown that there is a Banach space with...

Let X be a closed subspace of a Banach space W and let F be the operator ideal of finite-rank operators. If α is a tensor norm, A is a Banach operator ideal, and λ > 0, then we call the condition “‖S‖α ≤ λ‖S‖A(X,W ) for all S ∈ F(X,X)” an inner inequality and the condition “‖T‖α ≤ λ‖T‖A(Y,W ) for all Banach spaces Y and for all T ∈ F(Y,X)” an outer inequality. We describe cases when outer inequ...