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math.FA2009★ 4 cited
Some Classical and Recent Results Concerning Renorming Theory
Amanollah Assadi, Hadi Haghshenas
The problems connected with equivalent norms lie at the heart of Banach space theory. This is a short survey on some recent as well as classical results and open problems in renorm…
math.FA2008
A Review on Some Geometric Results of the Smulian s Theorem on Frechet Differentiability of Norms
A. Assadi, Hadi Haghshenas, H. Hosseini Guive
In this paper, we prove the Smulian s theorem on Frechet differentiability of norm,and present some of its geometric results concerning the Gateaux and Frechet differentiability of…
math.FA2008
Convexity of Chebyshev Sets Through Differentiability of Distance Function
A. Assadi, H. Haghshenas, H. Hosseini Guive
In this paper, we study a part of approximation theory that presents the conditions under which a \Ceby\sev set in a Banach space is convex. To do so, we use Gateaux differentiabil…