Convergence of approximating paths to solutions of variational inequalities involving non-Lipschitzian mappings

다국어 초록 (Multilingual Abstract)

Let X be a real reflexive Banach space with a uniformly
Gateaux differentiable norm, C a nonempty closed convex subset of X, T :
C → X a continuous pseudocontractive mapping, and A : C → C a
continuous strongly pseudocontractive mapping. We show the existence
of a path {xt} satisfying xt = tAxt+(1-t)Txt, t ∈ (0, 1) and prove that
{xt} converges strongly to a fixed point of T, which solves the variational
inequality involving the mapping A. As an application, we give strong
convergence of the path {xt} defined by xt = tAxt +(1-t)(2I-T)xt to
a fixed point of firmly pseudocontractive mapping T.

다국어 초록 (Multilingual Abstract)

Let X be a real reflexive Banach space with a uniformly
Gateaux differentiable norm, C a nonempty closed convex subset of X, T :
C → X a continuous pseudocontractive mapping, and A : C → C a
continuous strongly pseudocontractive mapping. We show the existence
of a path {xt} satisfying xt = tAxt+(1-t)Txt, t ∈ (0, 1) and prove that
{xt} converges strongly to a fixed point of T, which solves the variational
inequality involving the mapping A. As an application, we give strong
convergence of the path {xt} defined by xt = tAxt +(1-t)(2I-T)xt to
a fixed point of firmly pseudocontractive mapping T.

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