CONTRACTION-MAPPING ALGORITHM FOR THE EQUILIBRIUM PROBLEM OVER THE FIXED POINT SET OF A NONEXPANSIVE SEMIGROUP | Zendy

Trinh Ngoc Hai | Zendy; Le Qung Thuy | Zendy

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CONTRACTION-MAPPING ALGORITHM FOR THE EQUILIBRIUM PROBLEM OVER THE FIXED POINT SET OF A NONEXPANSIVE SEMIGROUP

Author(s) -

Trinh Ngoc Hai,

Le Qung Thuy

Publication year - 2018

Publication title -

mathematical modelling and analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.491

H-Index - 25

eISSN - 1648-3510

pISSN - 1392-6292

DOI - 10.3846/mma.2019.004

Subject(s) - mathematics , fixed point , semigroup , monotonic function , convergence (economics) , lipschitz continuity , contraction (grammar) , fixed point theorem , pure mathematics , algorithm , discrete mathematics , mathematical analysis , medicine , economics , economic growth

In this paper, we consider the proximal mapping of a bifunction. Under the Lipschitz-type and the strong monotonicity conditions, we prove that the proximal mapping is contractive. Based on this result, we construct an iterative process for solving the equilibrium problem over the fixed point sets of a nonexpansive semigroup and prove a weak convergence theorem for this algorithm. Also, some preliminary numerical experiments and comparisons are presented. First Published Online: 21 Nov 2018

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