JP Journal of Fixed Point Theory and Applications

Pushpa Publishing House

Submit Article

THE MODIFIED THREE STEP NOOR ITERATIVE SCHEME FOR FOUR MAPPINGS WITH RETRACTION

Authors

  • Clement Boateng Ampadu

Keywords:

Noor iterative scheme, Opial’s condition, I-quasi nonexpansive map.

DOI:

https://doi.org/10.17654/0973422822004

Abstract

In this paper, we establish the weak convergence of the sequence of modified three step Noor iterates to a common fixed point of four maps $T1$, $T2$, $T3$ and $I$.

Received: November 27, 2022
Accepted: December 29, 2022

References

W. V. Petryshyn and T. E. Williamson, Jr., A necessary and sufficient condition for the convergence of a sequence of iterates for quasinonexpansive mappings, Bull. Amer. Math. Soc. 78 (1972), 1027-1031.

F. Tricomi, Un teorema sulla convergenza delle successioni formate delle successivo iterate di una funzione di una variable reale, Giorn. Mat. Battaglini 54 (1916), 1-9.

J. B. Diaz and F. T. Metcalf, On the set of subsequential limit points of successive approximations, Trans. Amer. Math. Soc. 135 (1969), 459-485.

W. G. Dotson, Jr., On the Mann iterative process, Trans. Amer. Math. Soc. 149(1) (1970), 65-73.

J. B. Baillon, Un théorème de type ergodique pour les contractions non linéaires dans un espace de Hilbert (French), C. R. Acad. Sci. Paris Sér. A-B 280, No. 22, Aii (1975), A1511-A1514.

M. K. Ghosh and L. Debnath, Approximating common fixed points of families of quasi-nonexpansive mappings, Internat. J. Math. Math. Sci. 18(2) (1995), 287-292.

W. A. Kirk, Remarks on approximation and approximate fixed points in metric fixed point theory, Annales Universitatis Mariae Curie-Sklodowska, Section A 51(2) (1997), 167-178.

B. Xu and M. A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002), 444-453.

B. E. Rhoades and Seyit Temir, Convergence theorems for I-nonexpansive mapping, Inter. J. Math. Math. Sci. (2006), Article ID 63435, 1-4.

H. Kiziltunc and M. Ozdemir, On convergence theorem for nonself I-non expansive mapping in Banach spaces, Appl. Math. Sci. 1(48) (2007), 2379-2383.

P. Kumam, W. Kumethong and N. Jewwaiworn, Weak convergence theorems of three-step Noor iterative scheme for I-quasi-nonexpansive mappings in Banach spaces, Appl. Math. Sci. 2(59) (2008), 2915-2920.

Published

2023-01-03

Issue

Section

Articles