New perturbed iterations for a generalized class of strongly nonlinear operator inclusion problems in Banach spaces.
New versions of the Fan-Browder fixed point theorem and existence of economic equilibria.
New versions on Nikaidô's coincidence theorem
In 1959, Nikaidô established a remarkable coincidence theorem in a compact Hausdorff topological space, to generalize and to give a unified treatment to the results of Gale regarding the existence of economic equilibrium and the theorems in game problems. The main purpose of the present paper is to deduce several generalized key results based on this very powerful result, together with some KKM property. Indeed, we shall simplify and reformulate a few coincidence theorems on acyclic multifunctions,...
Newton's methods for variational inclusions under conditioned Fréchet derivative
Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and ω-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.
Nielsen number and differential equations.
Nonautonomous functional equations and nonlinear evolution operators
Noncompact perturbation of nonconvex noncompact sweeping process with delay
We prove an existence theorem of solutions for a nonconvex sweeping process with nonconvex noncompact perturbation in Hilbert space. We do not assume that the values of the orient field are compact.
Non-compact perturbations of -accretive operators in general Banach spaces
In this paper we deal with the Cauchy problem for differential inclusions governed by -accretive operators in general Banach spaces. We are interested in finding the sufficient conditions for the existence of integral solutions of the problem , , where is an -accretive operator, and is a continuous, but non-compact perturbation, satisfying some additional conditions.
Non-compact random generalized games and random quasi-variational inequalities.
Non-convex perturbations of evolution equations with -dissipative operators in Banach spaces
Nonconvex sets and fixed points
Nonexpansive mappings and convex sequences
Nonexpansive mappings and iterative methods in uniformly convex Banach spaces.
Nonexpansive mappings defined on unbounded domains.
Non-expansive mappings in spaces of continuous functions.
Nonexpansive maps in generalized Orlicz spaces
Nonexpansive retractions in Hilbert spaces
Let H be a Hilbert space and C ⊂ H be closed and convex. The mapping P: H → C known as the nearest point projection is nonexpansive (1-lipschitzian). We observed that, the natural question: "Are there nonexpansive projections Q: H → C other than P?" is neglected in the literature. Also, the answer is not often present in the "folklore" of the Hilbert space theory. We provide here the answer and discuss some facts connected with the subject.
Nonexpansive retracts in Banach spaces
We study various aspects of nonexpansive retracts and retractions in certain Banach and metric spaces, with special emphasis on the compact nonexpansive envelope property.
Nonlinear contractive conditions: A comparison and related problems
We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...
Nonlinear diffusion equations with perturbation terms on unbounded domains
This paper considers the initial-boundary value problem for the nonlinear diffusion equation with the perturbation term in an unbounded domain with smooth bounded boundary, where , , , is a single-valued maximal monotone function on , e.g., and is a function on which can be regarded as a Lipschitz continuous operator from to . The present work establishes existence and estimates for the above problem.