Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces. (11th March 2014)

• Record Type: Journal Article
• Authors: Bozkurt, Hacer; Çakan, Sümeyye; Yılmaz, Yılmaz
• Other Names: Braack Malte Academic Editor.
• Is Part Of: International journal of analysis. Volume 2014(2014)
• Publication Date: 2014-03-11
• Subjects: Mathematical analysis -- Periodicals; 515.05
• DOI: 10.1155/2014/258389
• Languages: English
• ISSNs: 2314-498X

Abstract

Abstract : Aseev launched a new branch of functional analysis by introducing the theory of quasilinear spaces in the framework of the topics of norm, bounded quasilinear operators and functionals (Aseev (1986)). Furthermore, some quasilinear counterparts of classical nonlinear analysis that lead to such result as Frechet derivative and its applications were examined deal with. This pioneering work causes a lot of results in such applications such as (Rojas-Medar et al. (2005), Talo and Başar (2010), and Nikol'skiĭ (1993)). His work has motivated us to introduce the concept of quasilinear inner product spaces. Thanks to this new notion, we obtain some new theorems and definitions which are quasilinear counterparts of fundamental definitions and theorems in linear functional analysis. We claim that some new results related to this concept provide an important contribution to the improvement of quasilinear functional analysis.