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In this work, it is assumed that the norm over bicomplex numbers is the hyperbolic (픻 -valued) norm. In this paper, we provide an overview of bicomplex Lebesgue spaces and investigate some of their geometric properties, including 픹 ⁢ ℂ -convexity, 픹 ⁢ ℂ -strict convexity, and 픹 ⁢ ℂ -uniform convexity. Moreover, the basic inequalities such as 픻 -Hölder's inequality and 픻 -Minkowski inequality for bicomplex Lebesgue spaces are presented, used to show geometric properties. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the notions of the Köthe–Toeplitz duals of sequence spaces by introducing the concepts of bicomplex α-dual, bicomplex β-dual and bicomplex γ-dual, and also we compute them for some bicomplex sequence spaces l p ⁢ ( 픹 ⁢ ℂ ) {l_{p}(\mathbb{BC})} for 1 ≤ p ≤ ∞ {1\leq p\leq\infty} , c 0 ⁢ ( 픹 ⁢ ℂ ) {c_{0}(\mathbb{BC})} and c ⁢ ( 픹 ⁢ ℂ ) {c(\mathbb{BC})} . Furthermore, we define a concept of bicomplex multiplier space as the bicomplex version of multiplier space of two sequence spaces and support this definition with examples. [ABSTRACT FROM AUTHOR]

In this paper, we examine the validity of bicomplex versions of some crucial inequalities with respect to the hyperbolic-valued norm | ⋅ | 한 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 ∥ ⋅ ∥ 픻 , ⋅ by defining the concept of 픻 -normed Banach bicomplex A-module and constructing 픻 -normed Banach bicomplex 픹 ⁢ ℂ -modules l p 한 ⁢ (픹 ⁢ ℂ) . [ABSTRACT FROM AUTHOR]

In this paper, we present Hölder’ s and Minkowski’s inequalities with Euclidean norm in the set of bicomplex numbers and define bicomplex sequence spaces. We also investigate the completeness property of our bicomplex sequence spaces using these Hölder’ s and Minkowski’ s inequalities. [ABSTRACT FROM AUTHOR]

In this work we introduce new spaces m² (F, φ, p) of double sequences defined by a double sequence of modulus functions, and we study some properties of this space. [ABSTRACT FROM AUTHOR]

The aim of this paper is to define a new class of Segal algebras, denoted by Wp,q, and to examine their some properties. [ABSTRACT FROM AUTHOR]