An algorithm for computing zeros of generalized phi-strongly monotone and bounded maps in classical Banach spaces. (English) Zbl 06587787
Summary: Let \(E=L_p\), \(1<p<\infty\), and \(A:E\to E^\ast\) be a generalized \(\Phi\)-strongly monotone and bounded map with \(A^{-1}(0)\neq\emptyset\). An iterative process is constructed and proved to converge strongly to the unique solution of the equation \(Au=0\). In the special case in which \(A\) is the subdifferential of a proper convex function \(f\), a solution of \(Au=0\) corresponds to a minimizer of \(f\). Furthermore, our technique of proof is of independent interest.
MSC:
| 47H04 | Set-valued operators |
| 47H06 | Nonlinear accretive operators, dissipative operators, etc. |
| 47H15 | Equations involving nonlinear operators [See also 58E07 for abstract bifurcation theory] (MSC1991) |
| 47H17 | Methods for solving equations involving nonlinear operators [See also 58C15] [For numerical analysis, see 65J15] (MSC1991) |
| 47J25 | Iterative procedures involving nonlinear operators |
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