Nearest and farthest points in nonlinear semi inner product spaces

Subject Areas : Statistics

Hamid Mazaheri ¹ , mohamad jafar salehi ² , Saeid Alikhani ³

1 - Professor, Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran
2 - Ph.D. Student, Department of Mathematics, Payame Noor University, Tehran, Iran
3 - Professor, Department of Mathematical Sciences, Yazd University, 89195-741, Yazd, Iran

Received: 2019-11-10 Accepted : 2022-10-10 Published : 2022-03-21

Keywords: نزدیکترین نقاط, مجموعه خورشیدی, دورترین نقاط, فضاهای نیم ضرب داخلی غیرخطی, مجموعه دوگان منفی,

Abstract :

In this paper, we first introduce the nearest and the farthest points in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the farthest points in linear spaces. we introduce the nearest and the farthest points in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the farthest points in linear spaces. we bring the nearest and the farthest points in linear spaces. we introduce the nearest and the farthest points in normed spaces, then introduce nonlinear semi inner product spaces, negative dual sets and sun sets. We make statements about these concepts. Define the concept of orthogonality of the nonlinear semi inner product and describe its properties. Finally, we bring the nearest and the farthest points in linear spaces.

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