Biquasilinear Functionals on Quasilinear Spaces and Some Related Results

Year 2020, , 95 - 104, 20.03.2020

Hacer Bozkurt , Yılmaz Yılmaz

https://doi.org/10.18185/erzifbed.664675

Abstract

In this paper, we will present the notion of the biquasilinear functional which is a new concept of quasilinear functional analysis. Just like bilinear functional, the notions of a biquasilinear functional and a quadratic form do not want to the constitution of an inner product quasilinear space. We were able to define these functionals in any quasilinear space. After giving this new notion, we discuss some examples and prove some theorems for considerable exercises to the theory of biquasilinear functionlas in Hilbert quasilinear spaces.

Keywords

Biquasilinear functional, quasilinear functional, quasilinear space, normed quasilinear space, inner product quasilinear space

Quasilineer Uzaylarda Biquasilineer Fonksiyoneller ve Bazı Sonuçları

Abstract

Bu çalışmada quasilineer fonksiyonel analizde yeni bir kavram olan
biquasilineer fonksiyonel kavramını tanımladık. Bilineer fonksiyonel kavramında
olduğu gibi biquasilineer fonksiyonel ve kuadratik form kavramlarında da bir iç
çarpım quasilineer uzayına ihtiyaç duyulmadığını gördük.  Bu fonksiyonelleri herhangi bir quasilineer
uzayında tanımlayabildik. Çalışmamızda bu yeni kavramı verdikten sonra Hilbert
quasilineer uzaylarda biquasilineer fonksiyoneller teorisi üzerine dikkate
değer bazı örnekler verdik. Ve yine bu teori üzerine bazı teoremler ve
ispatlarını çalışmamızda sunduk.

Keywords

Biquasilineer fonksiyonel, quasilineer fonksiyonel, quasilineer uzay, normlu quasilineer uzay, iç çarpım quasilineer uzayı

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