4 years ago

Riesz Lemma in Normed Quasilinear Spaces and Its an Application

Yılmaz Yılmaz, Sümeyye Çakan


Aseev (Proc Steklov Inst Math 2:23–52, 1986) started a new field in functional analysis by introducing the concept of normed quasilinear spaces which is a generalization of classical normed linear spaces. Then, we introduced the normed proper quasilinear spaces in addition to the notions of regular and singular dimension of a quasilinear space, Çakan and Yılmaz (J Nonlinear Sci Appl 8:816–836, 2015). In this study, we classify the normed proper quasilinear spaces as “solid-floored” and “non solid-floored”. Thus, some properties of normed proper quasilinear spaces become more comprehensible. Also we present the counterpart of classical Riesz lemma in normed quasilinear spaces.

Publisher URL: https://link.springer.com/article/10.1007/s40010-017-0418-x

DOI: 10.1007/s40010-017-0418-x

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