Fixed Point Results for Some Enriched Contractions in Convex B-Metric Spaces

S.  Yakubu; I. G.  Bassi; M. A.  Mbah

doi:10.5281/zenodo.20467595

S. Yakubu Department of Mathematics, Federal University of Lafia, Lafia, Nasarawa State, Nigeria.
I. G. Bassi Department of Mathematics, Federal University of Lafia, Lafia, Nasarawa State, Nigeria.
M. A. Mbah Department of Mathematics, Federal University of Lafia, Lafia, Nasarawa State, Nigeria.

DOI: https://doi.org/10.5281/zenodo.20467595

Keywords: Fixed point, Krasnoselskii's iterative method, Hardy- Rogers contraction, B- metric spaces.

Abstract

In this study, we show the existence of fixed points for enriched contractions and enriched ϕ-contractions of Hardy-Rogers type using Krasnoselskii's iterative process. Furthermore, we show that our results imply related fixed- point results for enriched contractions and enriched ϕ - contractions of Banach, Kannan, Chatterjea and Reich types. Our results are novel for convex b- metric spaces and generalize several established results in convex metric spaces.

References

V. Berinde, iterative approximation of fixed points, 2nd ed. Springer, 2007, pp. 15-16.

M. Krasnoselskii, "Two remarks on the method of successive approximations," uspehi Mat. Nauk., vol. 10, no. 1, pp. 123-127, 1955.

W. Takahashi, "Convexity in metric space and non-expansive mappings," Kodai Math. Sem. Rep., vol. 22, no. 2, pp. 142-149, 1970. [Online]. Available: https://doi.org/10.2996/kmj/1138846111.

O. J. Omidire, "Common fixed point theorems of some certain generalized contractive conditions in convex metric space settings," International Journal of Mathematical Sciences and Optimization: Theory and Applications, vol. 10, no. 3, pp. 1-9, 2024. [Online]. Available: https://doi.org/10.6084/zenodo.13152753.

S. Czerwik, "Contraction mappings in b- metric spaces," Acta Mathematica et Informatica Universitatis Ostraviensis, vol. 1, no. 1, pp. 5-11, 1993.

L. Chen, C. Li, R. Kaczmarek, and Y. Zhao, "Several fixed point theorems in convex b- metric spaces and applications," Mathematics, vol. 8, p. 242, 2020. [Online]. Available: https://doi.org/10.3390/math8020242.

G. Akinbo and O. O. Fabelurin, "Convergence of implicit noor iteration in convex b- metric space," International Journal of Mathematical Sciences and Optimization: Theory and Applications, vol. 11, no. 1, pp. 89-95, 2025.

S. Banach, "Sur les op' erations dans les ensembles abstraits et leurs applications aux ' equations int' egales," Fundamental Mathematics, vol. 3, pp. 133-181, 1922.

G. Hardy and T. Rogers, "A generalization of fixed point theorem of Reich," Canada Math. Bull., vol. 16, no. 2, pp. 201-206, 1973. [Online]. Available: https://doi.org/10.4153/CMB-1973-036-0.

V. Berinde and M. Pacurar, "Existence and approximation of fixed points of enriched contractions and enriched contractions," Symmetry, vol. 13, no. 3, 2021. [Online]. Available: https://doi.org/10.3390/sym13030498.

R. Kannan, "Some results on fixed point," Bull. Calcutta math. soc., vol. 60, 1968.

S. Chatterjea, "Fixed point theorems," C.R. Acad. Bulgare Sci., vol. 30, pp. 737-740, 1972.

S. Reich and I. Shafrir, "Nonexpansive iterations in hyperbolic spaces," Nonlinear Anal., vol. 15, no. 6, pp. 537-558, 1990. [Online]. Available: https://doi.org/10.1016/0362-546X(90)90058-O.