The purpose of this paper is to present new hybrid Ishikawa iteration process by the generalized f-projection operator for finding a common element of the fixed point set for two countable families of weak relatively nonexpansive mappings and the set of solutions of the system of generalized Ky...

The purpose of this paper is to show that the iterative scheme recently studied by Xu (J Glob Optim 36(1):115–125, <CitationRef CitationID="CR8">2006</CitationRef>) is the same as the one studied by Kamimura and Takahashi (J Approx Theory 106(2):226–240, <CitationRef CitationID="CR2">2000</CitationRef>) and to give a supplement to these results. With the new technique proposed...</citationref></citationref>

In this paper we consider the contraction-proximal point algorithm: <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${x_{n+1}=\alpha_nu+\lambda_nx_n+\gamma_nJ_{\beta_n}x_n,}$$< /EquationSource> </InlineEquation> where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${J_{\beta_n}}$$</EquationSource> </InlineEquation> denotes the resolvent of a monotone operator A. Under the assumption that lim<Subscript> n </Subscript> α <Subscript> n </Subscript> = 0, ∑<Subscript> n </Subscript> α <Subscript> n </Subscript> = ∞, lim inf<Subscript> n </Subscript> β <Subscript> n...</subscript></subscript></subscript></subscript></subscript></subscript></equationsource></inlineequation></equationsource></inlineequation>