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We present several fixed point theorems for monotone nonlinear operators in ordered Banach spaces. The main assumptions of our results are formulated in terms of the weak topology. As an application, we study the existence of solutions to a class of first-order vectorvalued ordinary differential equations. Our conclusions generalize many well-known results.

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In this paper, we find sufficient conditions for existence and uniqueness of fixed and coincidence points for infinite sequence of mappings satisfying some certain contractive conditions in what so called the generalized metric, G-metric, spaces.

Abstract. We consider a smoothly bounded q-pseudoconvex domain Ω in an ndimensional Stein manifold X and suppose that the boundary bΩ of Ω satisfies (q − P) property, which is the natural variant of the classical P property. Then, one prove the compactness estimate for the ∂-Neumann operator Nr,s in the Sobolev kspace. Applications to the boundary global regularity for the ∂-Neumann operator Nr,s in the Sobolev k-space are given. Moreover, we prove the boundary global regularity of the ∂-operator on Ω.