Esnek Biquasilineer Dönüşümler Aracılığıyla Esnek Operatör Teorisinde Quasilineer ve Bilineer Operatörler Arasında Köprü Kurma

Abstract

Bu çalışmada, esnek bilineer operatörler ile klasik bilineer operatörler arasındaki ilişki bir örnek kul-lanılarak gösterilmektedir. Daha sonra, klasik biquasilineer operatörler kavramını esnek ortama genişleten esnek biquasilineer operatörleri tanıtıyoruz. Birkaç esnek biquasilineer operatör incelenerek önemli bulgulara ulaşılmaktadır. Ek olarak, klasik fonksiyonel analizde olduğu gibi, her esnek quasilineer iç çarpımın bir esnek biquasilineer operatör oluşturduğu gösterilmektedir. Bunun yanında, söz konusu operatörler arasındaki ilişkiler küçük bir tablo hâlinde özetlenmiştir. Tüm esnek biquasilineer fonksiyonların kümesini Λ(Q ̃^2,(Ω_C (R)) ̃) ile gösteriyoruz ve uygun şekilde tanımlanmış bir norm ile donatıldığında bu kümenin bir esnek normlu quasilineer uzay ve dahası bir Banach quasilineer uzay oluşturduğunu gösteriyoruz. Ek olarak, esnek biquasilineer operatörlerin simetrisi ve pozitifliği analiz edilmekte ve ilgili birkaç teorem oluşturulmaktadır; böylece, esnek operatör teorisi ve esnek fonksiyonel analizinde daha ileri gelişmeler için sağlam bir temel sağlanmaktadır. Bu sonuçlar, esnek yaklaşımın avantajlarını ve uygulanabilirliğini ortaya koymakta; böylece daha ileri teorik gelişmeler ve pratik uygulamalar için temel oluşturmaktadır.

Keywords

• Esnek küme
• esnek quasilineer uzay
• esnek normlu quasilineer uzay
• esnek quasilineer operatör
• esnek biquasilineer operatör

Supporting Institution

Yazarlar, bu çalışmanın araştırma, yazarlık veya yayınlanması için herhangi bir mali destek almadıklarını beyan ederler.

Ethical Statement

Yazarlar bu çalışmanın herhangi bir etik kurul onayına veya özel izne ihtiyaç duymadığını beyan ederler.

Bridging Quasilinear and Bilinear Operators with Soft Operator Theory via Soft Biquasilinear Mappings

Abstract

In this paper, the relationship between soft bilinear operators and classical bilinear operators is illustrated using an example. We then introduce soft biquasilinear operators, which extend the concept of classical biquasilinear operators to the soft setting. Several soft biquasilinear operators are examined, leading to important findings. In addition, as in classical functional analysis, we observe that every soft quasilinear inner product gives rise to a soft biquasilinear operator. Moreover, the relationships among these operators are summarized in a small table. We denote the set of all soft biquasilinear functions by Λ(Q ̃^2,(Ω_C (R)) ̃), and we show that when equipped with a suitably defined norm, this set forms a soft normed quasilinear space and, moreover, a Banach quasilinear space. Additionally, the symmetry and positivity of soft biquasilinear operators are analyzed, and several related theorems are established, thereby providing a solid foundation for further developments in soft operator theory and soft functional analysis. These results demonstrate the advantages and applicability of the soft framework, thereby laying the foundation for further theoretical developments and practical applications.

Keywords

• Soft set
• soft quasilinear space
• soft normed quasilinear space
• soft quasilinear operator
• soft biquasilinear operator

Supporting Institution

The authors declare that no financial support was received for the research, authorship, or publication of this study.

Ethical Statement

The authors declare that this study does not require any ethics committee approval or special permission.

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