Resolvent Iterative Methods for Difference of Two Monotone Operators
نویسندگان
چکیده
In this paper, we consider the problem of finding a zero of difference of two monotone operators in Hilbert space. Using the resolvent operator technique, we establish the equivalence between the variational inclusions and the fixed point problems. This alternative equivalent formulation is used to suggest and analyze a two-step iterative method for solving the variational inclusions involving the difference of two monotone operators. We also show that the variational inclusions are equivalent to the resolvent equations. This equivalence formulation enables us to suggest and analyze a number of iterative methods. We consider the convergence analysis of these proposed iterative methods under suitable conditions. Our method of proofs are very simple as compared with other techniques. Several special cases are also discussed. AMS Subject Classification. 49J40, 90C33
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