Investigating the Relationship between Ordinary and Fuzzy Inner Product Spaces

Subject Areas : Numeric Analyze

Nasim Gholami ¹ , Saeid Abbasbandy ² , Nasrin Karamikabir ³

1 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran
2 - Department of Applied Mathematics, Imam Khomeini International University, Ghazvin, Iran
3 - Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

Received: 2020-05-12 Accepted : 2022-12-29 Published : 2022-08-23

Keywords: همگرای فازی, هسته بازتولید فازی, فضای هیلبرت فازی,

Abstract :

In this paper, we study the relationship between ordinary inner product spaces and fuzzy inner product spaces. We introduce fuzzy inner product as ⟨.,.⟩(.). Also, we write norm by parameter. Here are some types of arbitrary spaces. We show that these spaces are fuzzy inner product spaces. Furthermore, we investigate fuzzy convergence, fuzzy Cauchy, fuzzy complete and fuzzy Hilbert in the space W^m [0,1] by fuzzy inner space which is in the form ⟨.,.⟩(.). We study relationship between ordinary Hilbert space and fuzzy Hilbert space. Then we give a new definition of the fuzzy reproducing kernel property, where fuzzy inner product is by parameter λ. The properties of the fuzzy reproducing kernel are completely discussed in this paper. We study relationship between ordinary Hilbert space and fuzzy Hilbert space. Then we give a new definition of the fuzzy reproducing kernel property, where fuzzy inner product is by parameter λ. The properties of the fuzzy reproducing kernel are completely discussed in this paper.

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