New Iteration Scheme for Approximating a Common Fixed Point of a Finite Family of Mappings

F. O. Isiogugu, C. Izuchukwu, C. C. Okeke and Aftab Hussain

Journal of Mathematics, 2020, vol. 2020, 1-14

Abstract: 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 ςnin=1∞i=1N, the condition that ∑i=1Nςni=1, for each n≥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.

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:3287968

DOI: 10.1155/2020/3287968

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