A hybrid of the extragradient method and proximal point algorithm for inverse strongly monotone operators and maximal monotone operators in Banach spaces. (English) Zbl 1117.49011

Summary: We introduce two iterative sequences for finding a point in the intersection of the zero set of a inverse strongly monotone or inverse-monotone operator and the zero set of a maximal monotone operator in a uniformly smooth and uniformly convex Banach space. We prove weak convergence theorems under appropriate conditions, respectively.


49J40 Variational inequalities
90C52 Methods of reduced gradient type
49M30 Other numerical methods in calculus of variations (MSC2010)
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