The fixed point and Mann iterative of a kind of higher order singular Teodorescu operator

Abstract

First, we discuss the Hölder continuity for a kind of higher order singular Teodorescu operator in and estimate its norm. Next, we introduce a modified higher order Teodorescu operator and show that the operator has a unique fixed point by the Banach’s Contraction Mapping Principle. Finally, we prove that the Mann iterative sequence strongly converges to the fixed point of and gives an iterative sequence of the solution of a kind of singular integral equation.

Keywords:

• higher order singular Teodorescu operator
• Hölder continuity
• fixed point theorem
• Mann iterative sequence

AMS Subject Classifications:

• 30E20
• 30E25
• 45E05

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Science Foundation of China [grant number 11401159], [grant number 11301136], [grant number 11401162]; the Science Foundation of Hebei Province [grant number A2014208158] and the foundation of Hebei University of Science and Technology [grant number QD201028].