TY - JOUR
T1 - An iterative method for common solution to various problems
AU - Karahan, Ibrahim
AU - Khan, Safeer H
PY - 2019/7/1
Y1 - 2019/7/1
N2 - In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for demicontinuous nearly nonexpansive mappings. We prove that our method converges strongly to a common solution of all above problems. It is worth noting that Main Theorem is proved without usual demiclosedness condition. As our iterative method generalizes several methods, the results here improve and extend many recent results.
AB - In this paper, we introduce a new iterative method to find a common solution of a generalized mixed equilibrium problem, a variational inequality problem and a hierarchical fixed point problem for demicontinuous nearly nonexpansive mappings. We prove that our method converges strongly to a common solution of all above problems. It is worth noting that Main Theorem is proved without usual demiclosedness condition. As our iterative method generalizes several methods, the results here improve and extend many recent results.
KW - Generalized mixed equilibrium problem
KW - Hierarchical fixed point
KW - Nearly nonexpansive mapping
KW - Projection method
KW - Variational inequality
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U2 - 10.17777/ascm2019.29.3.349
DO - 10.17777/ascm2019.29.3.349
M3 - Article
SN - 1229-3067
VL - 29
SP - 349
EP - 364
JO - Advanced Studies in Contemporary Mathematics (Kyungshang)
JF - Advanced Studies in Contemporary Mathematics (Kyungshang)
IS - 3
ER -