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Behzad Djafari-Rouhani,Mohammad Farid,Kaleem Raza Kazmi 대한수학회 2016 대한수학회지 Vol.53 No.1
In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.
DJAFARI-ROUHANI, BEHZAD,FARID, MOHAMMAD,KAZMI, KALEEM RAZA Korean Mathematical Society 2016 대한수학회지 Vol.53 No.1
In this paper, we introduce and study an explicit hybrid relaxed extragradient iterative method to approximate a common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converges strongly to the common solution to generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, improvement and generalization of the previously known results in this area.
An iterative method for common solution to various problems
IBRAHIM KARAHAN,SAFEER HUSAIN KHAN 장전수학회 2019 Advanced Studies in Contemporary Mathematics Vol.29 No.3
In this paper, we introduce a new iterative method to nd a common solution of a generalized mixed equilibrium problem, a vari- ational inequality problem and a hierarchical xed 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 demiclosed- ness condition. As our iterative method generalizes several methods, the results here improve and extend many recent results.
Some iterative algorithms for the generalized mixedequilibrium-like problems
Zeqing Liu,Zhengsheng Chen,강신민 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
In this paper, we introduce and analyze a new class of generalized mixed equilibrium-like problems. By using the auxiliary principle technique, we suggest three iterative algorithms for the generalized mixed equilibrium-like problem. Under certain conditions, we establish the convergence of the iterative algorithms. Our results extend, improve and unify several known results in this field.
JUNG, JONG SOO Korean Mathematical Society 2015 대한수학회지 Vol.52 No.6
In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.
정종수 대한수학회 2015 대한수학회지 Vol.52 No.6
In this paper, we introduce a new iterative algorithm for finding a common element of the set of solutions of a generalized mixed equilibrium problem related to a continuous monotone mapping, the set of solutions of a variational inequality problem for a continuous monotone mapping, and the set of fixed points of a continuous pseudocontractive mapping in Hilbert spaces. Weak convergence for the proposed iterative algorithm is proved. Our results improve and extend some recent results in the literature.
EXISTENCE RESULTS FOR NEW GENERALIZED MIXED EQUILIBRIUM AND FIXED POINT PROBLEMS IN BANACH SPACES
Olawale Kazeem Oyewole,Oluwatosin Temitope Mewomo 경남대학교 수학교육과 2020 Nonlinear Functional Analysis and Applications Vol.25 No.2
In this paper, existence and uniqueness results for the solution of a new classof equilibrium problem is established. Using the KKM technique, we establish the existenceand uniqueness of solutions of a new generalized mixed equilibrium problem (NGMEP) withtrifunctions. Further, we propose an iterative algorithm for finding a common element inthe solution set of the NGMEP and a fixed point set of a nonlinear mapping. We provedthe strong convergence of the algorithm to a common element in the solution set of a systemof NGMEP and a fixed point set of a countable family of totally quasi-φ-asymptoticallynonexpansive mapping in the framework of a real uniformly convex and uniformly smoothBanach space. Our result generalize many other results obtained recently in this direction.