On Thakur iteration for $$L_2$$-operators with qualitative analysis

Abstract In this paper, we set out to explore a class of operators satisfying the condition $$L_2$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>L</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:math> , and check for their Fejér monotone convergence, and weak convergence. Moreover, qualitative studies related to a stability and data dependence analysis are presented. Meaningful comparisons with other numerical algorithms are provided, from the point of view of the convergence speed or CPU time. Additionally, a polynomiographic study is carried out to visually and quantitatively showcase how efficiently the proposed iterative process works.