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2013•Journal of Inequalities and ApplicationsOpen access

Approximating fixed points for a reversible semigroup of Lipschitzian mappings in a smooth Banach space

Hossein Piri, Poom Kumam

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Abstract

In this paper, we approximate a fixed point of the semigroup ϕ = {T s : s ∈ S} of Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition and with respect to a finite family of sequences {μ i,n } m, ∞ i=1,n=1 of left strong regular invariant means defined on an appropriate invariant subspace of l ∞ (S).Our result extends the main results announced by several others.

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In this paper, we approximate a fixed point of the semigroup ϕ = {T s : s ∈ S} of Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition and with respect to a finite family of sequences {μ i,n } m, ∞ i=1,n=1 of left strong regular invariant means defined on an appropriate invariant subspace of l ∞ (S).Our result extends the main results announced by several others.

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Available abstract

In this paper, we approximate a fixed point of the semigroup ϕ = {T s : s ∈ S} of Lipschitzian mappings from a nonempty compact convex subset C of a smooth Banach space E into C with a uniform Lipschitzian condition and with respect to a finite family of sequences {μ i,n } m, ∞ i=1,n=1 of left strong regular invariant means defined on an appropriate invariant subspace of l ∞ (S).Our result extends the main results announced by several others.

Key concepts: Mathematics, Banach space, Regular polygon, Fixed point, Semigroup, Invariant (physics), Pure mathematics, Invariant subspace

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