Displaying similar documents to “A sharp condition for the Loewner equation to generate slits.”

Convergence conditions for Secant-type methods

Ioannis K. Argyros, Said Hilout (2010)

Czechoslovak Mathematical Journal

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We provide new sufficient convergence conditions for the convergence of the secant-type methods to a locally unique solution of a nonlinear equation in a Banach space. Our new idea uses recurrent functions, and Lipschitz-type and center-Lipschitz-type instead of just Lipschitz-type conditions on the divided difference of the operator involved. It turns out that this way our error bounds are more precise than earlier ones and under our convergence hypotheses we can cover cases where earlier...

Infinitely many solutions of a second-order p -Laplacian problem with impulsive condition

Libo Wang, Weigao Ge, Minghe Pei (2010)

Applications of Mathematics

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Using the critical point theory and the method of lower and upper solutions, we present a new approach to obtain the existence of solutions to a p -Laplacian impulsive problem. As applications, we get unbounded sequences of solutions and sequences of arbitrarily small positive solutions of the p -Laplacian impulsive problem.