Picard-like Iteration Process for a Finite Family of Contractions
Agatha Chizoba Nnubia *
Department of Mathematics, Nnamdi Azikiwe University, P. M. B. 5025, Awka, Anambra State, Nigeria.
Chika Moore
Department of Mathematics, Nnamdi Azikiwe University, P. M. B. 5025, Awka, Anambra State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Let E be a metric space and let {\(\mathit{T}\)\(\mathit{i}\)}N be a finite family of contractions on E. It is proved that a picard-like iteration process converges to a point \(\mathit{x}\)* \(\in\) E if and only if \(\mathit{x}\)* is the common fixed point of the finite family {\(\mathit{T}\)\(\mathit{i}\)}N.
Keywords: Metric space, contractions, fixed point, strong convergence
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References
Picard E.Sur lWetude de certaines equations diferentielles ordinaries. J. Math. 1893;9:217-271.
Banach S. Theorie des operations lineires. Varsaw; 1932.
Cacciopoli R. Un teorem generealle sullWesistenza di elementi uniti in una trans- formazione funzionale. Rend. Accad. Na:,. Lincei. 1931;13:498-502.
Okereke CE. Fixed point and the contraction mapping principle with application to nonlinear integral equation of radiative transfer. Advances in Natural and Applied Sciences. 2009;3(2):170-8.
Nnubia AC, Akabuike MAN. Strong Convergence Theorem of a Viscosity Process for Finite Family of Total Asymptotically Nonexpansive Maps. JP Journal of Fixed Point Theory and Applications. 2019;14(2):51- 75.
Agarawal RP, Aksoy U, Karapman E, Erthan M. F- Contraction Mappings on Metric-like spaces in connection with Integral Equations on Time Scales; RACSAM. 2020;114 -147.
Georgiev S. Integral Equations on Time scales; Atlantis Press, Paris; 2016.
Hidefumi K. Nowhere- Di erentiable Function { an Application of Contraction Mappings. The American Mathematical Monthly. 1998;98(5):411-416.
Wardowski D. Solving Exstence Problem Via F- Contractins; Proc. Ams. 2018;146:1585-1598.
Wardowski D. Fixed Point of a New Type of Contractive Mappings in a Complete Metric Spaces, Fixed Point Theory nod Application. 2012;94.