In this paper we introduce the φ A-differentiability for functions f: U⊂ R k→ R n, where U is
an open set, A is the linear space R n endowed with a unital associative commutative …

The methods involving the functions analytic in a complex plane for plane potential fields
inspire the search for the analogous efficient methods for solving the spatial and …

The statement that any two-dimensional algebra 𝔹* of the second rank with unity over the
field of complex numbers contains such a basis {e 1; e 2} that 𝔹*-valued “analytic” functions …

Among all two-dimensional algebras of the second rank with unit e over the field of complex
numbers ℂ, we find a semisimple algebra 𝔹0:={c 1 e+ c 2𝜔: ck 𝜖 ℂ, k= 1, 2}, 𝜔2= e …

For monogenic (continuous and differentiable in the sense of Gâteaux) functions given in
special real subspaces of an arbitrary finitedimensional commutative associative algebra …

A class of H-analytic (differentiable by Hausdorff) functions in a three-dimensional
noncommutative algebra e A~ 2 over the field ℂ is considered. All H-analytic functions are …

On differentiable and monogenic functions in a harmonic algebra Page 1 Збiрник праць Iн-ту
математики НАН України 2017, том 14, № 1, 210–221 УДК 517.5 SA Plaksa (Institute of …

In finite-dimensional commutative associative algebra, the concept of σ-monogenic function
is introduced. Necessary and sufficient conditions for σ-monogeneity have been established …

In this paper, we consider some three-dimensional noncommutative algebra A~ 2 over the
field C, which contains the algebra of bicomplex numbers B (C) as a subalgebra. Locally …

This chapter discusses the concepts of differentiable function Φ: Ω→ 𝔸 taking values in a
vector space 𝔸 in which a commutative multiplication is defined for most of its elements, and …