Necessary conditions on composition operators acting on Sobolev spaces of fractional order. The critical case 1 ... s ... n/p.
Neumann and periodic boundary-value problems for quasilinear ordinary differential equations with a nonlinearity in the derivative.
New class of boundary value problem for nonlinear fractional differential equations involving Erdélyi-Kober derivative
In this paper, we introduce a new class of boundary value problem for nonlinear fractional differential equations involving the Erdélyi-Kober differential operator on an infinite interval. Existence and uniqueness results for a positive solution of the given problem are obtained by using the Banach contraction principle, the Leray-Schauder nonlinear alternative, and Guo-Krasnosel'skii fixed point theorem in a special Banach space. To that end, some examples are presented to illustrate the usefulness...
New existence theorems of positive solutions for singular boundary value problems.
New fixed point free nonexpansive maps on weakly compact, convex subsets of L¹[0,1]
We show that every subset of L¹[0,1] that contains the nontrivial intersection of an order interval and finitely many hyperplanes fails to have the fixed point property for nonexpansive mappings.
New fixed point theorems of mixed monotone operators and applications to singular boundary value problems on time scales.
New hybrid iterative schemes for an infinite family of nonexpansive mappings in Hilbert spaces.
New iteration methods for asymptotically nonexpansive mappings in uniformly smooth real Banach spaces
New iteration methods for pseudocontractive and accretive operators in arbitrary Banach spaces
New iterative approximation methods for a countable family of nonexpansive mappings in Banach spaces.
New iterative scheme for finite families of equilibrium, variational inequality, and fixed point problems in Banach spaces.
New iterative schemes for asymptotically quasi-nonexpansive mappings.
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.