Abstract
AbstractIn this paper, we study an iterative scheme for two different types of resolvents of a monotone operator defined on a Banach space. These resolvents are generalizations of resolvents of a monotone operator in a Hilbert space. We obtain iterative approximations of a zero point of a monotone operator generated by the shrinking projection method with errors in a Banach space. Using our result, we discuss some applications.
Highlights
Let H be a real Hilbert space and let A ⊂ H × H be a maximal monotone operator
The set of zero points of A is denoted by A–. This problem is connected with many problems in Nonlinear Analysis and Optimization, that is, convex minimization problems, variational inequality problems, equilibrium problems and so on
We obtain an iterative approximation of a zero point of a monotone operator generated by the shrinking projection method with errors in a Banach space
Summary
Let H be a real Hilbert space and let A ⊂ H × H be a maximal monotone operator. the zero point problem is to find u ∈ H such that ∈ Au. ( . )Such a u ∈ H is called a zero point (or a zero) of A. We obtain an iterative approximation of a zero point of a monotone operator generated by the shrinking projection method with errors in a Banach space.
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