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Weak convergence in L1 of the sequences of monotonic functions

Puchała P.

Journal of Applied Mathematics and Computational Mechanics

2014

Vol. 13, nr 3

195--199

We use (quasi-) Young measures associated with strictly monotonic functions with a differentiable inverse to prove an L1 ([0,1],ℝ) weak convergence of the monotonic sequence of such functions. The result is well known, but the method seems to be new.

Weak convergence for nonself nearly asymptotically nonexpansive mappings by iterations

Khan S. H.

Demonstratio Mathematica

2014

Vol. 47, nr 2

371--381

In this paper, we obtain a couple of weak convergence results for nonself nearly asymptotically nonexpansive mappings. Our first result is for the Banach spaces satisfying Opial condition and the second for those whose dual satisfies the Kadec-Klee property.

A note on the weak convergence of a sequence of successive approximations

Kalinde A., Mishra S., Singh S.

Demonstratio Mathematica

2006

Vol. 39, nr 3

619-624

In this paper we discuss the weak convergence of the sequence of successive approximations for a generalized para-nonexpansive mapping in a reflexive Banach space that satisfies Opial's condition.