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Assume that is continuous strongly pseudocontractive mapping.
In particular a contraction cocycle whose Markov semigroup is norm continuous strongly satisfies a QSDE.
It is easy to see that the mapping Ws,t: C → C is a continuous strongly pseudocontractive mapping.
This result was subsequently generalized by Deimling [4] to the continuous strongly accretive operators (see, e.g., Deimling [[5], Theorem 13.1]).
Schu [2] generalized the result in [1] to both uniformly continuous strongly pseudo-contractive mappings and real smooth Banach spaces.
Let C be a nonempty closed convex subset of a Banach space X and T : C → C a continuous strongly pseudo-contractive mapping.
Similar(38)
Let X be a reflexive real Banach space, let (Phi, Psi:X rightarrowmathbb{R}) be two Gâteaux differentiable functionals such that Φ is sequentially weakly lower semi-continuous, strongly continuous, and coercive, and Ψ is sequentially weakly upper semi-continuous.
Since A is weakly-strongly continuous, converges strongly to Ax. Consequently (3.34).
A Lipschitz continuous and strongly monotone mapping is a strongly monotone mapping.
If the gradient ∇g is Lipschitz continuous and strongly monotone, then the sequence generated by (1.3) and (1.4) can converge strongly to a minimizer of (1.2).
The mapping (C_{i}: D(C_{i})subset W_{i} rightarrow W_{i}) is continuous and strongly accretive.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com