New method for computing zeros of monotone maps in lebesgue spaces with applications to integral equations, fixed points, optimization, and variational inequality problems
ACTA MATHEMATICA UNIVERSITATIS COMENIANAE(2022)
Abstract
Let E = L-p, 1 < p <= 2, and A: E -> E* be a bounded monotone map such that 0 & ISIN; R(A). In this paper, we introduce and study an algorithm for approximating zeros of A. Furthermore, we study the application of this algorithm to the approximation of Hammerstein integral equations, fixed points, convex optimization, and variational inequality problems. Finally, we present numerical and illustrative examples of our results and their applications.
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Key words
Monotone operators,strong convergence,Lp spaces,Hammerstein in-tegral equations,fixed points,convex optimization,variational inequality
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