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Fixed point theorems for metrically weakly inward set-valued mappings

Ding X. P., He Y. R.

Journal of Applied Analysis

1999

Vol. 5, nr 2

283-293

In this paper, the concept of metrically weakly inward set-valued mappings is introduced. The relationship between the metrically weakly inward mappings and other inward type mappings is considered in normed spaces. A positive answer of the Caristi's open problem is given. These results generalize the cor-responding results in recent literature.

Set-valued implicit Wiener-Hopf equations and generalized strongly nonlinear quasivariational inequalities

Ding X. P.

Journal of Applied Analysis

1998

Vol. 4, nr 1

75-87

In this paper, we study a class of generalized strongly nonlinear quasivariational inequality problem (GSNQVIP(T,A,g,D,K(x))) which include the most of quasivariational inequalities and quasicomplementarity problems as special cases. We prove that the generalized strongly nonlinear quasivariational inequality problem is equivalent to solving the set-valued implicit Wiener-Hopf equation. By using the equivalence, a new iterative algorithm for finding the approximate solutions of the generalized strongly nonlinear quasivariational inequality problems are suggested and analyzed. The convergence criteria for the algorithm is also discussed. These new results include many known results for generalized quasivariational inequalities and generalized quasicomplementarity problems as special cases.