The mappings A and S are faintly compatible (take a constant sequence y n = 2 5 ) and they commute at the coincidence point at x = 2 5.
The mappings A, (Phi_{1}), (Phi_{2}), and Ψ are uniformly Lipschitz continuous with respect to ((lambda,xi)), x, ((x,p)), and y, respectively.
For any (yinmathbb{R}^{m}), (Psi y)inmathbb{R}^{m}). (ii) The mappings A, (Phi_{1}), (Phi_{2}), and Ψ are uniformly Lipschitz continuous with respect to ((lambda,xi)), x, ((x,p)), and y, respectively. .
In this section, using Theorem 2.3, we obtain some new strong convergence results for the class of mappings, a quasi-nonexpansive mapping and a nonexpansive mapping in a Hilbert space.
It is worth to mention that fixed point theory for nonexpansive mappings, a limit case of a contraction mapping when the Lipschitz constant is allowed to be 1, requires tools far beyond metric fixed point theory.
Furthermore, we observe that any α-inverse strongly monotone mappings A is a monotone and (frac{1}{alpha} -Lipschitzian mapping.
In 1969, the Banach's Contraction Mapping Principle extended nicely to set-valued or multivalued mappings, a fact first noticed by Nadler [6].
Mapping difficulties fell into 4 categories: 1) One-to-many mappings: a common problem, especially when eukaryotic host proteins derived from alternate splicing or viral polyproteins are involved.
Remark 2.4 Faint compatibility is a necessary condition for the existence of common fixed points of given mappings A and S satisfying contractive or more general Lipschitz-type mapping pairs.
