Novel extended Halpern-type convergence algorithms for the split common fixed point problem involving α-demicontractive operators

Abstract

As is well known, it is quite valuable and challenging to solve the split common fixed point problem (SCFP) associated with two different nonlinear operators. In this study, in order to solve (SCFP) with a more general setting of α-demicontractive operators due to Măruşter and Măruşter in 2011, we develop a kind of novel iterative approach in infinite dimensional Hilbert spaces. Further, using Xu's inequality and Maingé's lemma, strong convergence theorems of the suggested algorithms are established under some mild conditions. Finally, some special cases are considered, and the main results of this work are supported via two numerical comparisons.

Keywords:

• Strong convergence
• novel extended Halpern-type iterative algorithm
• split common fixed point problem
• α-demicontractive operator
• infinite dimensional Hilbert space

Mathematics Subject Classifications:

• 47J25
• 47H10
• 47H09

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Innovation Fund of Postgraduate, Sichuan University of Science & Engineering (Y2022188).