Abstract
Abstract In this paper, we introduce both explicit and implicit schemes for finding a common element in the common fixed point set of a one-parameter nonexpansive semigroup {T(s)| 0 ≤ s < ∞} and in the solution set of an equilibrium problems which is a solution of a certain optimization problem related to a strongly positive bounded linear operator. Strong convergence theorems are established in the framework of Hilbert spaces. As an application, we consider the optimization problem of a k-strict pseudocontraction mapping. The results presented improve and extend the corresponding results of many others. 2000 AMS Subject Classification: 47H09; 47J05; 47J20; 47J25.
Highlights
Let H be a real Hilbert space with inner product 〈·,·〉 and norm || · ||
It is clear that T(s)T(t) = T(s + t) = T(t)T(s) for s, t ≥ 0
Motivated by the ongoing research and the above mentioned results, we introduce both explicit and implicit schemes for finding a common element in the common fixed point set of a one-parameter nonexpansive semigroup {T(s)|0 ≤ s
Summary
Let H be a real Hilbert space with inner product 〈·,·〉 and norm || · ||. Recall, a mapping T with domain D(T) and range R(T) in H is called nonexpansive iff for all x, y Î D(T),. Lemma 1.4 Let C be a nonempty bounded closed convex subset of a Hilbert space H and I = {T(t): 0 ≤ t 0 on H, I = {T(s): s ≥ 0} be a nonexpansive semigroup on C, respectively. Let F a bifunction from C × C ® R satisfying (A1)-(A4), f be a weakly contractive mapping with a function on H, A a strongly positive linear bounded operator with coefficient γ > 0 on H, and T be a nonexpansive mapping from C into itself, respectively. Our results contain the ones in [23] and [27] as special cases
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