Algebraic properties of bihyperbolic numbers

M Bilgin, S Ersoy - Advances in Applied Clifford Algebras, 2020 - Springer
In this paper, we study the four-dimensional real algebra of bihyperbolic numbers. Under
consideration of the spectral representation of the bihyperbolic numbers, we give a partial …

Topological bicomplex modules

R Kumar, H Saini - Advances in applied Clifford algebras, 2016 - Springer
In this paper, we develop topological modules over the ring of bicomplex numbers. We
discuss bicomplex convexity, hyperbolic-valued seminorms and hyperbolic-valued …

Integration of functions of a hyperbolic variable

ME Luna-Elizarrarás - Complex Analysis and Operator Theory, 2022 - Springer
This paper presents a systematic study of the theory of integration of hyperbolic-valued
functions from a new point of view where the notion of partial order defined on the set of …

Some fundamental theorems of functional analysis with bicomplex and hyperbolic scalars

H Saini, A Sharma, R Kumar - Advances in Applied Clifford Algebras, 2020 - Springer
We discuss some properties of linear functionals on topological hyperbolic and topological
bicomplex modules. The hyperbolic and bicomplex analogues of the uniform boundedness …

[PDF][PDF] Fixed points of hyperbolic contraction mappings on hyperbolic valued metric spaces

N Sager, B Sağır - Sarajevo Journal of Mathematics, 2021 - researchgate.net
In this paper, we give some elementary topological concepts and results on hyperbolic
valued metric space and then, we introduce two fixed point theorems for hyperbolic valued …

[PDF][PDF] Some new identities with respect to bihyperbolic Fibonacci and Lucas numbers

AZ Azak - International Journal of Sciences: Basic and Applied …, 2021 - researchgate.net
In this paper, we define bihyperbolic Lucas numbers, bihyperbolic generalized Fibonacci
numbers and give some algebraic properties of these numbers. Then, some identities …

Hyperbolic conformality in multidimensional hyperbolic spaces

A Golberg, ME Luna‐Elizarrarás - Mathematical Methods in the …, 2024 - Wiley Online Library
In a previous work, the hyperbolic conformality for bicomplex functions was introduced, and
it was proved that, with the adequate hypothesis, a bicomplex holomorphic function is …

Maximal ideals in a bicomplex algebra and bicomplex Gelfand–Mazur theorem

R Kumar, K Singh - Complex Variables and Elliptic Equations, 2022 - Taylor & Francis
In this paper, we study the maximal ideals in a commutative ring of bicomplex numbers and
then we describe the maximal ideals in a bicomplex algebra. We found that the kernel of a …

Zabreiko's Lemma with Bicomplex and hyperbolic scalars and its applications

AS Rane, M Thatte - arXiv preprint arXiv:2402.06631, 2024 - arxiv.org
In this paper, we shall consider the notion of hyperbolic semi norm which on a module $ X $
to set of all positive hyperbolic numbers. We shall prove the characterization of continuity of …

[PDF][PDF] Bicomplex Mergelyan's Approximation Theorem

A Ali, M Arif, R Kumar - arXiv preprint arXiv:2211.11340, 2022 - arxiv.org
arXiv:2211.11340v3 [math.FA] 5 Jun 2023 Page 1 BICOMPLEX MERGELYAN’S
APPROXIMATION THEOREMS AMJAD ALI, MOHD ARIF, AND ROMESH KUMAR Abstract. In …