New Inner Product Quasilinear Spaces on Interval Numbers

Abstract

Primarily we examine the new example of quasilinear spaces, namely, “IRninterval space.” We obtain some new theorems and results related to this new quasilinear space. After giving some new notions of quasilinear dependence-independence and basis on quasilinear functional analysis, we obtain some results onIRninterval space related to these concepts. Secondly, we presentIs,Ic0,Il∞, andIl2quasilinear spaces and we research some algebraic properties of these spaces. We obtain some new results and provide an important contribution to the improvement of quasilinear functional analysis.

Quasilineer Uzaylarda Biquasilineer Fonksiyoneller ve Bazı Sonuçları

“…Let be quasilinear space. A function 〈•,•〉: × → Ω (ℝ) is named an inner produt on if for every , , , ∈ and ∈ ℝ the next cases are provided: Yılmaz, 2016a).…”

“…For every two elements and of an inner product quasilinear space, we obtain ‖〈 , 〉‖ Ω (ℝ) ≤ ‖ ‖ ‖ ‖ . An inner product on quasilinear space defines a norm on given by ‖ ‖ = √ ‖〈 , 〉‖ Ω (ℝ) (Bozkurt and Yılmaz, 2016a).…”

“…A complete inner product quasilinear space is named a Hibert quasilinear space to the inner product norm (Bozkurt and Yılmaz, 2016a).…”

“…Since then, several papers have deal with quasilinear functional analysis or the setvalued analysis ( see, e.g., Rojas Medar et al, 2005;Alefeld and Mayer, 2000;Çakan and Yılmaz, 2015;Levent and Yılmaz, 2018b. ;Bozkurt and Yılmaz, 2016a;Bozkurt and Yılmaz, 2018b;Bozkurt and Yılmaz, 2018b;Laksmikantham et al, 2006).…”

Inner Product Fuzzy Quasilinear Spaces and Some Fuzzy Sequence Spaces

“…Furthermore, he presented some results which are "quasilinear" counterparts of fundamental de nitions and theorems in linear functional analysis and di erential calculus in Banach spaces. is pioneering work has motivated a lot of authors to introduce new results on multivalued mappings, fuzzy quasilinear spaces and operators, and set-valued analysis [8][9][10][11][12][13][14]. In this way, Rojas Medar et al [6] introduced the concept of fuzzy quasilinear spaces and de ned the notion of a norm on these spaces.…”