Weak Parallelogram Laws for Banach Spaces

Weak parallelogram laws on banach spaces and applications to prediction

This paper concerns a family of weak parallelogram laws for Banach spaces. It is shown that the familiar Lebesgue spaces satisfy a range of these inequalities. Connections are made to basic geometric ideas, such as smoothness, convexity, and Pythagorean-type theorems. The results are applied to the linear prediction of random processes spanning a Banach space. In particular, theweak parallelogr...

Weak Interpolation in Banach Spaces

Weak Thresholding Greedy Algorithms in Banach Spaces

We consider weak thresholding greedy algorithms with respect to Markushevich bases in general Banach spaces. We find sufficient conditions for the equivalence of boundedness and convergence of the approximants. We also show that if there is a weak thresholding algorithm for the system which gives the best n-term approximation up to a multiplicative constant, then the system is already “greedy”....

Weak convergence theorems for symmetric generalized hybrid mappings in uniformly convex Banach spaces

‎In this paper‎, ‎we prove some theorems related to properties of‎ ‎generalized symmetric hybrid mappings in Banach spaces‎. ‎Using Banach‎ ‎limits‎, ‎we prove a fixed point theorem for symmetric generalized‎ ‎hybrid mappings in Banach spaces‎. ‎Moreover‎, ‎we prove some weak‎ ‎convergence theorems for such mappings by using Ishikawa iteration‎ ‎method in a uniformly convex Banach space.

Weak convergence theorem for Lipschitzian pseudocontraction semigroups in Banach spaces

In this work, theorems of weak convergence of an implicit iterative algorithm with errors for treating a nonexpansive semigroup and a Lipschitzian pseudocontractive semigroup are estabilshed in the framework of real Banach spaces. 2010 Mathematics Subject Classification. Primary 60J05; Secondary 60J20.