We give the bicomplex Gaussian Fibonacci and Lucas numbers establish generating functions Binet’s formulas related to these numbers. Also, we present summation formula, matrix representation Honsberger identity their relationship between Finally, show relationships among Fibonacci, Lucas,

Using three different representations of the bicomplex numbers T ∼= ClC(1, 0) ∼= ClC(0, 1), which is a commutative ring with zero divisors defined by T = {w0 + w1i1 + w2i2 + w3j | w0, w1, w2, w3 ∈ R} where i1 = −1, i 2 2 = −1, j 2 = 1 and i1i2 = j = i2i1, we construct three classes of bicomplex pseudoanalytic functions. In particular, we obtain some specific systems of Vekua equations of two co...

In this paper, we study some basic properties of bicomplex numbers. We introduce two different types partial order relations on numbers, discuss valued metric spaces with respect to orders, and compare them. also define a hyperbolic space, the density natural statistical convergence, Cauchy property sequence numbers investigate in space prove that is complete if only complex are complete.

In this article, we introduce the concept of normal families of bicomplex holomorphic functions to obtain a bicomplex Montel theorem. Moreover, we give a general definition of Fatou and Julia sets for bicomplex polynomials and we obtain a characterization of bicomplex Fatou and Julia sets in terms of Fatou set, Julia set and filled-in Julia set of one complex variable. Some 3D visual examples o...

Abstract Bicomplex convolutional neural networks (BCCNN) are a natural extension of the quaternion for bicomplex case. As it happens with quaternionic case, BCCNN has capability learning and modelling external dependencies that exist between neighbour features an input vector internal latent within feature. This property arises from fact that, under certain circumstances, is possible to deal nu...

in this paper, lie group structure and lie algebra structure of unit complex 3-sphere     are studied. in order to do this, adjoint representations of unit biquaternions (complexified quaternions) are obtained. also, a correspondence between the elements of     and the special complex unitary matrices    (2) is given by expressing biquaternions as 2-dimensional bicomplex numbers    .  the relat...

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

In this paper, we study the maximal ideals in a commutative ring of bicomplex numbers and then describe algebra. We found that kernel nonzero multiplicative BC-linear functional Banach algebra need not be ideal. Finally, introduce notion division generalize Gelfand–Mazur theorem for

A bicomplex is a simple mathematical structure, in particular associated with completely integrable models. The conditions defining a bicomplex are a special form of a parameter-dependent zero curvature condition. We generalize the concept of a Darboux matrix to bicomplexes and use it to derive Bäcklund transformations for several models. The method also works for Moyal-deformed equations with ...