New iteration scheme for approximating a common fixed point of a finite family of mappings (Q780470)

Summary: We introduce a new algorithm (horizontal algorithm) in a real Hilbert space, for approximating a common fixed point of a finite family of mappings, without imposing on the finite family of the control sequences \(\{\{\varsigma_n^i\}_{n = 1}^\infty\}_{i=1}^N\), the condition that \(\sum_{i=1}^N \varsigma_n^i = 1\), for each \(n\geq 1\). Furthermore, under appropriate conditions, the horizontal algorithm converges both weakly and strongly to a common fixed point of a finite family of type-one demicontractive mappings. It is also applied to obtain some new algorithms for approximating a common solution of an equilibrium problem and the fixed point problem for a finite family of mappings. Our work is a contribution to ongoing research on iteration schemes for approximating a common solution of fixed point problems of a finite family of mappings and equilibrium problems.