Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 14 4 2023 04 01 A novel approach for convergence and stability of Jungck-Kirk-Type algorithms for common fixed point problems in Hilbert spaces 297 312 6730 10.22075/ijnaa.2021.23396.2530 EN Lmo Kalu Agwu Department of Mathematics, Micheal Okpara University of Agriculture, Umudike, Umuahia Abia State, Nigeria 0000-0003-4535-1974 Donatus Ikechi Igbokwe Department of Mathematics, Micheal Okpara University of Agriculture, Umudike, Umuahia Abia State, Nigeria Journal Article 2021 03 11 In this paper, two novel iteration algorithms called Jungck-DI-Noor-multistep and Jungck-DI-SP-multistep iterative schemes are introduced and studied. Using their strong convergence, a common fixed point of nonself mappings was achieved without any imposition of 'sum conditions' on the control sequences. Further, we studied and proved the stability results of our new iterative schemes in the setting of a real Hilbert space. Our results improve, generalize and unify several known results currently in the literature. strong convergence Jungck-DI-Noor-multistep iterative scheme Jungck-DI-SP-multistep iterative scheme stability Contractive operator Common fixed point Real Hilbert space https://ijnaa.semnan.ac.ir/article_6730_4f884db81fd7fc684b021ee47f7626d9.pdf