A Krasnoselskiĭ cone compression result for multimaps in the S-KKM class.
A la recherche du spectre perdu: An invitation to nonlinear spectral theory
We give a survey on spectra for various classes of nonlinear operators, with a particular emphasis on a comparison of their advantages and drawbacks. Here the most useful spectra are the asymptotic spectrum by M. Furi, M. Martelli and A. Vignoli (1978), the global spectrum by W. Feng (1997), and the local spectrum (called “phantom”) by P. Santucci and M. Väth (2000). In the last part we discuss these spectra for homogeneous operators (of any degree), and derive a discreteness result and a nonlinear...
A Landesman-Lazer alternative theorem for a class of optimization problems.
A Leray--Schauder alternative for weakly-strongly sequentially continuous weakly compact maps.
A linear condition determining local or global existence for nonlinear problems
Given a nonlinear autonomous system of ordinary or partial differential equations that has at least local existence and uniqueness, we offer a linear condition which is necessary and sufficient for existence to be global. This paper is largely concerned with numerically testing this condition. For larger systems, principals of computations are clear but actual implementation poses considerable challenges. We give examples for smaller systems and discuss challenges related to larger systems. This...
A method for a solution of equilibrium problem and fixed point problem of a nonexpansive semigroup in Hilbert's spaces.
A minimax inequality with applications to existence of equilibrium point and fixed point theorems
Ky Fan’s minimax inequality [8, Theorem 1] has become a versatile tool in nonlinear and convex analysis. In this paper, we shall first obtain a minimax inequality which generalizes those generalizations of Ky Fan’s minimax inequality due to Allen [1], Yen [18], Tan [16], Bae Kim Tan [3] and Fan himself [9]. Several equivalent forms are then formulated and one of them, the maximal element version, is used to obtain a fixed point theorem which in turn is applied to obtain an existence theorem of an...
A minimization theorem in quasi-metric spaces and its applications.
A modification of Newton's method
A modified iterative process for common fixed points of two finite families of nonexpansive mappings.
A modulus for property (β) of Rolewicz
We define a modulus for the property (β) of Rolewicz and study some useful properties in fixed point theory for nonexpansive mappings. Moreover, we calculate this modulus in spaces for the main measures of noncompactness.
A Monotone Operator Method for the Solution of Fredholm Integral Equations.
-monotonicity and applications to nonlinear variational inclusion problems.
A multiplicity fixed point theorem in Fréchet spaces.
A multiplicity result for a system of real integral equations by use of the Nielsen number
We prove an existence and multiplicity result for solutions of a nonlinear Urysohn type equation (2.14) by use of the Nielsen and degree theory in an annulus in the function space.
A multivalued fixed point theorem in non-archimedean vector spaces.
A new approach to the existence results for orientor fields with Nicoletti's boundary conditions
Applying a global bifurcation theorem for convex-valued completely continuous mappings we prove some existence theorems for convex-valued differential inclusions of the form x'∈ F(t,x), where x satisfies the Nicoletti boundary conditions.
A new approximation method for common fixed points of a finite family of generalized asymptotically quasinonexpansive mappings in Banach spaces.
A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings.
A new approximation scheme combining the viscosity method with extragradient method for mixed equilibrium problems.