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
References
- Alefeld G., Mayer G., (2000). “Interval Analysis: Theory and Applications”, Jurnal of Computational and Applied Mathematics, (121),421-464.
- Aseev S.M., (1986). “Quasilinear operators and their application in the theory of multivalued mappings”, Proceeding of the Steklov Institute of Mathematics, (2),23-52.
- Banazılı H.K., (2014). “On Quasilinear Operators Between Quasilinear Spaces”, İnönü University Graduate School of Natural and Applied Sciences, Master Thesis (Printed).
- Bozkurt H., Yılmaz Y., (2016a). “New Inner Product Quasilinear Spaces on Interval Numbers”, Journal of Function Spaces, Vol. 2016, Article ID 2619271:9 pages.
- Bozkurt H., Yılmaz Y., (2016b). “Some New Results on Inner Product Qusilinear Spaces”, Cogent Mathematics, 3:1194801:10 pages.
- Bozkurt H., Yılmaz Y., (2016c). “On Inner Product Quasilinear Spaces and Hilbert Quasilinear Spaces”, Information Science and Computing, Vol. 2016, Article ID ISC671116:12 pages.
- Çakan S., Yılmaz Y., (2015). “Normed Proper Quasilinear Spaces”, Journal of Nonlinear Sciences and Applications, (8),816-836.
- Laksmikantham V., Gnana Bhaskar T., Vasundhara Devi J., (2006). “Theory of set differential equations in metric spaces”, Cambridge Scientic Publishers, Cambridge.
- Levent H., Yılmaz Y., (2018a). “Hahn-Banach extension theorem for interval-valued functions and existence of quasilinear functionals”, New Trends in Mathematical Sciences, NTMSC6(2),19-28.
- Levent H., Yılmaz Y., (2018b). “Translation, Modulation and Dilation Systems in Set-Valued Signal Processing”, Carpathian Mathematical Publications, 10(1),143-164.
- Rojas Medar M.A., Jimenez Gamerob M.D., Chalco Canoa Y., Viera Brandao A.J., (2005). “Fuzzy quasilinear spaces and applications”, Fuzzy Sets and Systems (152),173-190.
- Yılmaz Y., Bozkurt H., Çakan S., (2016). “On Orthonormal Sets in Inner Product Quasilinear Spaces”, Creative Mathematics and Informatics, 25(2)2, 237-247.
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
References
- Alefeld G., Mayer G., (2000). “Interval Analysis: Theory and Applications”, Jurnal of Computational and Applied Mathematics, (121),421-464.
- Aseev S.M., (1986). “Quasilinear operators and their application in the theory of multivalued mappings”, Proceeding of the Steklov Institute of Mathematics, (2),23-52.
- Banazılı H.K., (2014). “On Quasilinear Operators Between Quasilinear Spaces”, İnönü University Graduate School of Natural and Applied Sciences, Master Thesis (Printed).
- Bozkurt H., Yılmaz Y., (2016a). “New Inner Product Quasilinear Spaces on Interval Numbers”, Journal of Function Spaces, Vol. 2016, Article ID 2619271:9 pages.
- Bozkurt H., Yılmaz Y., (2016b). “Some New Results on Inner Product Qusilinear Spaces”, Cogent Mathematics, 3:1194801:10 pages.
- Bozkurt H., Yılmaz Y., (2016c). “On Inner Product Quasilinear Spaces and Hilbert Quasilinear Spaces”, Information Science and Computing, Vol. 2016, Article ID ISC671116:12 pages.
- Çakan S., Yılmaz Y., (2015). “Normed Proper Quasilinear Spaces”, Journal of Nonlinear Sciences and Applications, (8),816-836.
- Laksmikantham V., Gnana Bhaskar T., Vasundhara Devi J., (2006). “Theory of set differential equations in metric spaces”, Cambridge Scientic Publishers, Cambridge.
- Levent H., Yılmaz Y., (2018a). “Hahn-Banach extension theorem for interval-valued functions and existence of quasilinear functionals”, New Trends in Mathematical Sciences, NTMSC6(2),19-28.
- Levent H., Yılmaz Y., (2018b). “Translation, Modulation and Dilation Systems in Set-Valued Signal Processing”, Carpathian Mathematical Publications, 10(1),143-164.
- Rojas Medar M.A., Jimenez Gamerob M.D., Chalco Canoa Y., Viera Brandao A.J., (2005). “Fuzzy quasilinear spaces and applications”, Fuzzy Sets and Systems (152),173-190.
- Yılmaz Y., Bozkurt H., Çakan S., (2016). “On Orthonormal Sets in Inner Product Quasilinear Spaces”, Creative Mathematics and Informatics, 25(2)2, 237-247.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | March 20, 2020 |
| Published in Issue | Year 2020 Volume: 13 Issue: 1 |