Some inequalities in quasi-Banach algebra of non-Newtonian bicomplex numbers

Değirmen, Nilay; Sağır, Birsen

doi:10.2298/fil2107231s

Filomat

2021

DOI: 10.2298/fil2107231s

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Some inequalities in quasi-Banach algebra of non-Newtonian bicomplex numbers

Nilay Değirmen

Birsen Sağır

Abstract: In this paper, we construct the quasi-Banach algebra BC(N) of non-Newtonian bicomplex numbers and we generalize some topological concepts and inequalities as Schwarz?s, H?lder?s and Minkowski?s in the set of bicomplex numbers in the sense of non-Newtonian calculus.

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On bicomplex 𝔹ℂ-modules l_p ^𝕜(𝔹ℂ) and some of their geometric properties

Değirmen

Sağır

2022

Georgian Mathematical Journal

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In this paper, we examine the validity of bicomplex versions of some crucial inequalities with respect to the hyperbolic-valued norm | ⋅ | 𝕜 {|\cdot|_{\Bbbk}} and we discuss some topological and geometric concepts such as completeness, convexity, strict convexity and uniform convexity in the bicomplex setting with respect to the hyperbolic-valued norm ∥ ⋅ ∥ 𝔻 , ⋅ {\|\cdot\|_{\mathbb{D},\cdot}} by defining the concept of 𝔻 {\mathbb{D}} -normed Banach bicomplex A-module and constructing 𝔻 {\mathbb{D}} -normed Banach bicomplex 𝔹 ⁢ ℂ {\mathbb{BC}} -modules l p 𝕜 ⁢ ( 𝔹 ⁢ ℂ ) {l_{p}^{\Bbbk}(\mathbb{BC})} .

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On bicomplex 𝔹ℂ-modules l_p ^𝕜(𝔹ℂ) and some of their geometric properties

Değirmen

Sağır

2022

Georgian Mathematical Journal

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On -Continuity and -Uniform Continuity of Some Non-Newtonian Superposition Operators

Erdogan¹,

DUYAR²

2021

European Journal of Science and Technology

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Many studies have been done on superposition operators and non-Newtonian calculus from past to present. Sağır and Erdoğan defined Non-Newtonian superposition operators and characterized them on some sequence spaces. Also they examined *-boundedness and *locally boundedness of Non-Newtonian superposition operators c0,α and cα to l1,β. In this study, we define *-continuity and *-uniform continuity of operator. We have proved that the necessary and sufficient conditions for the *-continuity of the non-Newtonian superposition operator c0,α to l1,β. Then we examined the relationship between the *-uniform continuity and the *-boundedness of the non-Newtonian superposition operator. Also, the similar results have been researched for the Non-Newtonian superposition operator cα to l1,β.

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A Note on non-Newtonian Isometry

Ogur,

Gunes

2024

Wseas Transactions on Mathematics

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Some inequalities in quasi-Banach algebra of non-Newtonian bicomplex numbers

Abstract: In this paper, we construct the quasi-Banach algebra BC(N) of non-Newtonian bicomplex numbers and we generalize some topological concepts and inequalities as Schwarz?s, H?lder?s and Minkowski?s in the set of bicomplex numbers in the sense of non-Newtonian calculus.

Cited by 3 publications

References 0 publications

On bicomplex 𝔹ℂ-modules l_p ^𝕜(𝔹ℂ) and some of their geometric properties

On bicomplex 𝔹ℂ-modules l_p ^𝕜(𝔹ℂ) and some of their geometric properties

On -Continuity and -Uniform Continuity of Some Non-Newtonian Superposition Operators

A Note on non-Newtonian Isometry

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Resources

About

Some inequalities in quasi-Banach algebra of non-Newtonian bicomplex numbers

Abstract: In this paper, we construct the quasi-Banach algebra BC(N) of non-Newtonian bicomplex numbers and we generalize some topological concepts and inequalities as Schwarz?s, H?lder?s and Minkowski?s in the set of bicomplex numbers in the sense of non-Newtonian calculus.

Cited by 3 publications

References 0 publications

On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties

On bicomplex 𝔹ℂ-modules lp 𝕜(𝔹ℂ) and some of their geometric properties

On *-Continuity and *-Uniform Continuity of Some Non-Newtonian Superposition Operators

A Note on non-Newtonian Isometry

Contact Info

Product

Resources

About

On bicomplex 𝔹ℂ-modules l_p ^𝕜(𝔹ℂ) and some of their geometric properties

On bicomplex 𝔹ℂ-modules l_p ^𝕜(𝔹ℂ) and some of their geometric properties

On -Continuity and -Uniform Continuity of Some Non-Newtonian Superposition Operators