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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.

MSC:

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