A generalized section theorem and a minimax inequality for a vector-valued mapping 1

A generalized Fan's section theorem has proposed by replacing convexity assumptions with merely topological properties. A generalized reformulation of Browder's fixed point theorem has derived. The Minimax Inequalities for vector-valued mapping in an ordered Banach space have established without the convexity and with convexity, respectively.     

BROWDER AND SEMI-BROWDER OPERATORS＊

In this article,we study characterization,stability,and spectral mapping theorem for Browder's essential spectrum,Browder's essential defect spectrum and Browder's essential approximate point spectrum ...     

Nonlinear random elliptic boundary value problem

In this paper we obtain a solvability result for random elliptic boundary value problem. Our result extends Browder's [2] main theorem to the random case. We use author's [4] fixed point theorem for this purpose.     

KKM mappings in metric spaces

We introduce the class of KKM-type mappings on metric spaces and establish some fixed point theorems for this class. We also obtain a generalized Fan's matching theorem, a generalized Fan–Browder's type theorem, and a new version of Fan's best approximation theorem.     

Caratheodory-type selections and random fixed point theorems

We provide some new Caratheodory-type selection theorems, i.e., selections for correspondences of two variables which are continuous with respect to one variable and measurable with respect to the other. These results generalize simultaneously Michael's [21]continuous selection theorem for lower-semicontinuous correspondences as well as a Caratheodory-type selection theorem of Fryszkowski [10]. Random fixed point theorems (which generalize ordinary fixed point theorems, e.g., Browder's [6]) follow as easy corollaries of our results.     

Existence and generic stability of solutions for multiclass multicriteria traffic equilibrium problems with capacity constraints of arcs

ABSTRACT

In this paper, we introduce the multiclass multicriteria traffic equilibrium problem with capacity constraints of arcs and its equilibrium principle. Using Fan–Browder's fixed points theorem and Fort's lemma to prove the existence and generic stability results of multiclass multicriteria traffic equilibrium flows with capacity constraints of arcs.     

On a Parameterized System of Nonlinear Equations with Economic Applications

We study a parameterized system of nonlinear equations. Given a nonempty, compact, and convex set, an affine function, and a point-to-set mapping from the set to the Euclidean space containing the set, we constructively prove that, under certain (boundary) conditions on the mapping, there exists a connected set of zero points of the mapping, i.e., the origin is an element of the image for every point in the connected set, such that the connected set has a nonempty intersection with both the face at which the affine function is minimized and the face at which that function is maximized. This result generalizes and unifies several well-known existence theorems including Browder??s fixed point theorem and Ky Fan??s coincidence theorem. An economic application with constrained equilibria is also discussed.     

Coperturbation function and lower semi-Browder multivalued linear operators

In this article, we investigate the perturbation theory of lower semi-Browder and Browder linear relations. Our approach is based on the concept of a coperturbation function for linear relations in order to establish some perturbation theorems and deduce the stability under strictly cosingular operator perturbations. Furthermore, we apply the obtained results to study the invariance and the characterization of Browder's essential defect spectrum and Browder's essential spectrum.     

A Fixed Point Theorem of Krasnoselskii—Schaefer Type

In this paper we focus on three fixed point theorems and an integral equation. Schaefer's fixed point theorem will yield a T-periodic solution of (0.1) x(t)= a(t) + ^t_t-h D(t,s)g(s,x(s))ds if D and g satisfy certain sign conditions independent of their magnitude. A combination of the contraction mapping theorem and Schauder's theorem (known as Krasnoselskii's theorem) will yield a T-periodic solution of (0.2) x(t) = f(t,x(t)) + ^t_t-h D(t,s)g(s,x(s))ds if f defines a contraction and if D and g are small enough. We prove a fixed point theorem which is a combination of the contraction mapping theorem and Schaefer's theorem which yields a T-periodic solution of (0.2) when / defines a contraction mapping, while D and g satisfy the aforementioned sign conditions.     

Pseudo Asymptotically Periodic Solutions for Volterra Difference Equations of Convolution Type

In this paper, the author studies the existence and uniqueness of discrete pseudo asymptotically periodic solutions for nonlinear Volterra difference equations of convolution type, where the nonlinear perturbation is considered as Lipschitz condition or non-Lipschitz case, respectively. The results are a consequence of application of different fixed point theorems, namely, the contraction mapping principle, the Leray-Schauder alternative theorem and Matkowski''s fixed point technique.     

FIXED POINTS FOR WEAKLY INWARD MAPPINGS IN BANACH SPACES (Ⅱ)

S. Hu and Y. Sun[1] defined the fixed point index for weakly inward mappings, investigated its properties and studied fixed points for such mappings. In this paper, following S. Hu and Y. Sun, we further investigate boundary conditions, under which the fixed point index for i(A,Ω, p) is equal to nonzero, where i(A,Ω, p) is the completely continuous and weakly inward mapping. Correspondingly, we can obtain many new fixed point the-orems of the completely continuous and weakly inward mapping, which generalize...     

Existence,uniqueness, and multiplicity results on positive solutions for a class of Hadamard-type fractional boundary value problem on an infinite interval

This paper focuses on a class of Hadamard-type fractional differential equation with nonlocal boundary conditions on an infinite interval. New existence, uniqueness, and multiplicity results of positive solutions are obtained by using Schauder's fixed point theorem, Banach's contraction mapping principle, the monotone iterative method, and the Avery-Peterson fixed point theorem. Examples are included to illustrate our main results.     

Viscosity approximation methods for generalized equilibrium problems and fixed point problems

The purpose of this paper is to investigate the problem of finding a common element of the set of solutions of a generalized equilibrium problem (for short, GEP) and the set of fixed points of a nonexpansive mapping in the setting of Hilbert spaces. By using well-known Fan-KKM lemma, we derive the existence and uniqueness of a solution of the auxiliary problem for GEP. On account of this result and Nadler’s theorem, we propose an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping. Furthermore, it is proven that the sequences generated by this iterative scheme converge strongly to a common element of the set of solutions of GEP and the set of fixed points of a nonexpansive mapping.     

Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings

In this paper, we introduce an iteration process of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for an inverse strongly-monotone mapping, and then obtain a weak convergence theorem. Using this result, we obtain a weak convergence theorem for a pair of a nonexpansive mapping and a strictly pseudocontractive mapping. Further, we consider the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of an inverse strongly-monotone mapping.     

A fixed point theorem including the last theorem of Poincaré

Poincaré's last theorem is the most famous among those theorems which are not subsumed by the Lefschetz fixed point theorem. A fixed point theorem is proved directly and constructively which in a special case reduces to the last theorem of Poincaré.     

Strong Convergence Theorems for Variational Inequalities and Fixed Point Problems of Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense

The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of an asymptotically strict pseudocontractive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce a modified hybrid Mann iterative scheme with perturbed mapping which is based on well-known CQ method, Mann iteration method and hybrid (or outer approximation) method. We establish a strong convergence theorem for three sequences generated by this modified hybrid Mann iterative scheme with perturbed mapping. Utilizing this theorem, we also design an iterative process for finding a common fixed point of two mappings, one of which is an asymptotically strict pseudocontractive mapping in the intermediate sense and the other taken from the more general class of Lipschitz pseudocontractive mappings.     

Fractional Boundary Value Problems with Integral Boundary Conditions via Topological Degree Method

This paper examines the existence and uniqueness of solutions for the fractional boundary value problems with integral boundary conditions. Banach''s contraction mapping principle and Schaefer''s fixed point theorem have been used besides topological technique of approximate solutions. An example is propounded to uphold our results.     

A new iterative method for equilibrium problems and fixed point problems of infinitely nonexpansive mappings and monotone mappings

In this paper, we introduce a new iterative scheme for finding the common element of the set of common fixed points of infinitely many nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mapping in Hilbert spaces. We prove that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions. This main result improve and extend Plubtieng and Punpaeng’s corresponding result [S. Plubtieng, R. Punpaeng, A new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings, Applied Mathematics and Computation 197 (2008), 548–558]. Using this theorem, we obtain three corollaries.     

On interior regularity and Liouville's theorem for harmonic mappings

It is well known that the weakly harmonic mapping U∶M→N (M,N: Riemannian manifolds) is regular if the image U(M) is contained in some sufficiently small ball and for this case Liouville's theorem is valid. In this paper we show that the smallness condition for U(M) can be released if U minimizes the energy functional and the sectional curvatures of the target manifold N are bounded by some suitable function of the distance from some fixed point of N.     

Convergence analysis of a hybrid Mann iterative scheme with perturbed mapping for variational inequalities and fixed point problems

The purpose of this article is to investigate the problem of finding a common element of the set of fixed points of a non-expansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz continuous mapping. We introduce a hybrid Mann iterative scheme with perturbed mapping which is based on the well-known Mann iteration method and hybrid (or outer approximation) method. We establish a strong convergence theorem for three sequences generated by this hybrid Mann iterative scheme with perturbed mapping. Utilizing this theorem, we also construct an iterative process for finding a common fixed point of two mappings, one of which is non-expansive and the other taken from the more general class of Lipschitz pseudocontractive mappings.