Some properties of quasi-Cauchy-type singular integral operator on unbounded domains.

Firstly, this paper gives the Cauchy-type integral formula and the Plemelj formula of hypermonogenic functions on unbounded domains and discusses the Hölder continuity of the quasi-Cauchy-type singular integral operator for hypermonogenic functions on unbounded domains. Secondly, this paper studies the relation betweenandand introduces the modified quasi-Cauchy-type singular integral operator. Finally, this paper proves the existence and uniqueness of the fixed point of the operatorby the Banach’s Contraction Mapping Principle and gives a Mann iterative sequence which strongly converges to the fixed point of the operator. [ABSTRACT FROM AUTHOR]