Browsing by Author "Gunawan, Hendra"

Now showing 1 - 3 of 3
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    On Finite Dimensional 2-Normed Spaces
    (2016-02-17) Gunawan, Hendra; Mashadi
    In this note we shall study nite dimensional 􀀀 normed spaces and show that their topology can be fully described by using a certain norm derived from the 􀀀 norm Moreover we show that a 􀀀 Banach space is a Banach space and use this fact to prove the Fixed Point Theorem Our result extends to some in nite dimensional 􀀀 normed spaces
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    On n-normed spaces
    (2016-02-17) Gunawan, Hendra; Mashadi
    Given an n-normed space with n ≥ 2, we offer a simple way to derive an (n−1)- norm from the n-norm and realize that any n-normed space is an (n−1)-normed space. We also show that, in certain cases, the (n−1)-norm can be derived from the n-norm in such a way that the convergence and completeness in the n-norm is equivalent to those in the derived (n − 1)-norm. Using this fact, we prove a fixed point theorem for some n-Banach spaces
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    Orthogonality In 2-Normed Spaces Revisited
    (2016-02-17) Gunawan, Hendra; Mashadi; Gemawati, Sri; Nursupiamin; Sihwaningrum, Idha
    In this paper we discuss some existing notions of orthogonality in 2-normed spaces and their drawback. We also formulate new de¯nitions of orthogo- nality that improve the existing ones. In the standard 2-normed space, our notions of orthogonality coincide with the usual one.