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Let K be a nonempty closed convex subset of a real Banach space E and T be a Lipschitz pseudocontractive self-map of K with F (T) := {x ∈ K : T x = x} } = ∅. An iterative sequence {xn} is constructed for which ||xn − T xn|| → 0 as n → ∞. If, in addition, K is assumed to be bounded, this conclusion still holds without the requirement that F (T) = ∅.(More)
Recommended by Donal O'Regan Let E be a real Banach space, K a closed convex nonempty subset of E, and T 1 ,T 2 ,...,T m : K → K asymptotically quasi-nonexpansive mappings with sequences (resp.) {k in } ∞ n=1 satisfying k in → 1 as n → ∞, and ∞ n=1 (k in − 1) < ∞, i = 1,2,...,m. Let {α n } ∞ n=1 be a sequence in [, 1 − ], ∈ (0,1). Define a sequence {x n }(More)
Let H be a real Hilbert space. Let F : D(F) ⊆ H → H, K : D(K) ⊆ H → H be bounded monotone mappings with R(F) ⊆ D(K), where D(F) and D(K) are closed convex subsets of H satisfying certain conditions. Suppose the equation 0 = u + KF u has a solution in D(F). Then explicit iterative methods are constructed that converge strongly to such a solution. No(More)
Suppose X = Lp (or Ip), p > 2, and K is a nonempty closed convex bounded subset of X. Suppose T: K —* K is a Lipschitzian strictly pseudo-contractive mapping of K into itself. Let {Cn}^_0 be a real sequence satisfying: (i) 0 < C " < 1 for all n > 1, (") Z)rT=l Cn = °°> and Then the iteration process, zn G K, Zn+l = (1 — Cn)xn + CnTXn for n > 1, converges(More)
Let E be a q-uniformly smooth Banach space possessing a weakly sequentially continuous duality map (e.g., p, 1 < p < ∞). Let T be a Lipschitzian pseudocontractive selfmapping of a nonempty closed convex and bounded subset K of E and let ω ∈ K be arbitrary. Then the iteration sequence {zn} defined by z 0 ∈ K, z n+1 = (1 − µ n+1)ω + µ n+1 yn; yn = (1 − αn)zn(More)
In this paper, we consider a generalized mixed set-valued variational inequality problem which includes many important known variational inequality problems and equilibrium problem, and its related some auxiliary variational inequality problems. We prove the existence of solutions of the auxiliary variational inequality problems and suggest a two-step(More)