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    The method for solving the split equality variational inequality problem and application
    Some method is introduced to solve the split equality variational inequality problem and we also apply our result to find solution of the split equality fixed problem and the null point problem of maximal monotone which are introduced by Moudafi and Al-Shemas [A. Moudafi, E. Al-Shemas, Simultaneous iterative methods for split equality problem, Trans. Math. Program. Appl. 1 (2013) 1–11] and Chang and Agarwal [S.S. Chang, R.P. Agarwal, Strong convergence theorems of general split equality problems for quasi-nonexpansive mappings, Journal of Inequalities and Applications 2014 (2014) 367], respectively.
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    A new technique for coincidence point theory in metric spaces endowed with graph
    Coincidence theory is a generalization of fixed point theory. There are many researchs combining fixed point theory and graph theory. In this paper, a new type of multi-valued mapping and g-l-graph preserving is proposed to prove a coincidence point theorem on complete metric spaces endowed with a directed graph. Supported examples of there main theorems are also introduced. Main results are sufficiently conditions for finding a vertex in the directed graph such that itself image of the defined surjective mapping is contained in the defined multivalued mapping. The proposed theorem can be apply use to obtain the similar result in a matrix space endowed with a partial order set.
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    The split various variational inequalities problems for three hilbert spaces
    There are many methods for finding a common solution of a system of variational inequalities, a split equilibrium problem, and a hierarchical fixed-point problem in the setting of real Hilbert spaces. They proved the strong convergence theorem. Many split feasibility problems are generated in real Hillbert spaces. The open problem is proving a strong convergence theorem of three Hilbert spaces with different methods from the lasted method. In this research, a new split variational inequality in three Hilbert spaces is proposed. Important tools which are used to solve classical problems will be developed. The convergence theorem for finding a common element of the set of solution of such problems and the sets of fixed-points of discontinuous mappings has been proved.