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1.
A projected subgradient method for solving generalized mixed variational inequalities 总被引:1,自引:0,他引:1
We consider the projected subgradient method for solving generalized mixed variational inequalities. In each step, we choose an εk-subgradient uk of the function f and wk in a set-valued mapping T, followed by an orthogonal projection onto the feasible set. We prove that the sequence is weakly convergent. 相似文献
2.
In this paper, we introduce the hybrid method of modified Mann’s iteration for an asymptotically k-strict pseudo-contractive mapping. Then we prove that such a sequence converges strongly to PF(T)x0. This main theorem improves the result of Issara Inchan [I. Inchan, Strong convergence theorems of modified Mann iteration methods for asymptotically nonexpansive mappings in Hilbert spaces, Int. J. Math. Anal. 2 (23) (2008) 1135–1145] and concerns the result of Takahashi et al. [W. Takahashi, Y. Takeuchi, R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 341 (2008) 276–286], and many others. 相似文献
3.
A μ-algebra is a model of a first-order theory that is an extension of the theory of bounded lattices, that comes with pairs of terms (f,μx.f) where μx.f is axiomatized as the least prefixed point of f, whose axioms are equations or equational implications.Standard μ-algebras are complete meaning that their lattice reduct is a complete lattice. We prove that any nontrivial quasivariety of μ-algebras contains a μ-algebra that has no embedding into a complete μ-algebra.We then focus on modal μ-algebras, i.e. algebraic models of the propositional modal μ-calculus. We prove that free modal μ-algebras satisfy a condition–reminiscent of Whitman’s condition for free lattices–which allows us to prove that (i) modal operators are adjoints on free modal μ-algebras, (ii) least prefixed points of Σ1-operations satisfy the constructive relation μx.f=n≥0fn(). These properties imply the following statement: the MacNeille–Dedekind completion of a free modal μ-algebra is a complete modal μ-algebra and moreover the canonical embedding preserves all the operations in the class of the fixed point alternation hierarchy. 相似文献
4.
In this paper, we study the existence of periodic solutions for a fourth-order p-Laplacian differential equation with a deviating argument as follows:
[φp(u″(t))]″+f(u″(t))+g(u(t−τ(t)))=e(t).