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