Abstract
Abstract In this paper, we introduce two iterative algorithms for finding common solutions of a finite family of variational inclusions for maximal monotone and inverse-strongly monotone mappings with the constraints of two problems: a generalized mixed equilibrium problem and a common fixed point problem of an infinite family of nonexpansive mappings and an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions. MSC:49J30, 47H09, 47J20, 49M05.
Highlights
Let H be a real Hilbert space with inner product ·, · and norm ·, C be a nonempty closed convex subset of H and PC be the metric projection of H onto C
Inspired by the above facts, we in this paper introduce two iterative algorithms for finding common solutions of a finite family of variational inclusions for maximal monotone and inverse-strongly monotone mappings with the constraints of two problems: a generalized mixed equilibrium problem and a common fixed point problem of an infinite family of nonexpansive mappings and an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space
We prove some strong and weak convergence theorems for the proposed iterative algorithms under suitable conditions
Summary
Let H be a real Hilbert space with inner product ·, · and norm · , C be a nonempty closed convex subset of H and PC be the metric projection of H onto C. Inspired by the above facts, we in this paper introduce two iterative algorithms for finding common solutions of a finite family of variational inclusions for maximal monotone and inverse-strongly monotone mappings with the constraints of two problems: a generalized mixed equilibrium problem and a common fixed point problem of an infinite family of nonexpansive mappings and an asymptotically strict pseudocontractive mapping in the intermediate sense in a real Hilbert space. ]) Let C be a nonempty closed convex subset of a Hilbert space H and S : C → C be a continuous asymptotically κ-strict pseudocontractive mapping in the intermediate sense with sequence {γn}. ]) Let C be a nonempty closed convex subset of a Hilbert space H and S : C → C be a continuous asymptotically κ-strict pseudocontractive mapping in the intermediate sense with sequence {γn} such that Fix(S) = ∅. Lemma . ([ , p. ]) Let {an}∞ n= , {bn}∞ n= , and {δn}∞ n= be sequences of nonnegative real numbers satisfying the inequality an+ ≤ ( + δn)an + bn, ∀n ≥
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