In this paper, the Schwarz boundary value problem (BVP) for the inhomogeneous Cauchy-Riemann equation in a triangle is investigated explicitly. Firstly, by the technique of parquetingreflection and the Cauchy-Pompeiu representation formula a modified Cauchy-Schwarz representation formula is obtained. Then, the solution of the Schwarz BVP is explicitly solved. In particular, the boundary behavio...

In previous work the framework for a hypercomplex function theory in superspace was established and amply investigated. In this paper a Cauchy integral formula is obtained in this new framework by exploiting techniques from orthogonal Clifford analysis. After introducing Clifford algebra valued surfaceand volume-elements first a purely fermionic Cauchy formula is proven. Combining this formula ...

In this article, we first give a modified Schwarz–Pompeiu formula in general sector ring with angle \(\vartheta =\frac{\pi }{\alpha },\ \alpha \ge 1/2\) by proper conformal mappings, and obtain the solution of Schwarz problem for Cauchy–Riemann equation explicit forms. Furthermore, construct some integral operators discuss their properties detail. Finally, virtue these operators, problems an in...

We consider a two-sided Pompeiu type problem for discrete group G G . give necessary and sufficient conditions finite subset K"> <mml:mi...

In theoretical setting, associated with a fractional [Formula: see text]-Fueter operator that depends on an additional vector of complex parameters real parts, this paper establishes analog Borel–Pompeiu formula as first step to develop text]-hyperholomorphic function theory and the related calculus.

Let [unk] be a finite family of finite subsets of the n-dimensional lattice Z(n), and let tau denote the group of all translations of Z(n). We shall here consider the Pompeiu problem for the family [unk]-namely, to determine when the only function f:Z(n) --> C such that [Formula: see text] is the zero function.