Measures of noncircularity and fixed points of contractive multifunctions.
Measures of noncompactness and normal structure in Banach spaces
Sufficient conditions for normal structure of a Banach space are given. One of them implies reflexivity for Banach spaces with an unconditional basis, and also for Banach lattices.
Measures of noncompactness in locally convex spaces and fixed point theory for the sum of two operators on unbounded convex sets
In this paper we prove a collection of new fixed point theorems for operators of the form on an unbounded closed convex subset of a Hausdorff topological vector space . We also introduce the concept of demi--compact operator and -semi-closed operator at the origin. Moreover, a series of new fixed point theorems of Krasnosel’skii type is proved for the sum of two operators, where is -sequentially continuous and -compact while is -sequentially continuous (and -condensing, -nonexpansive or nonlinear contraction...
Measures of non-strict-singularity of operators
Meir-Keeler contractions of integral type are still Meir-Keeler contractions.
Metric fixed point theory for multivalued mappings [Book]
Metric spaces admitting only trivial weak contractions
If (X,d) is a metric space then a map f: X → X is defined to be a weak contraction if d(f(x),f(y)) < d(x,y) for all x,y ∈ X, x ≠ y. We determine the simplest non-closed sets X ⊆ ℝⁿ in the sense of descriptive set-theoretic complexity such that every weak contraction f: X → X is constant. In order to do so, we prove that there exists a non-closed set F ⊆ ℝ such that every weak contraction f: F → F is constant. Similarly, there exists a non-closed set G ⊆ ℝ such that every weak contraction...
Minimal displacement in Hilbert spaces
We give a lower bound for the minimal displacement characteristic in Hilbert spaces.
Minimax and Fixed Point Theorems.
Minimax inequality of Ky Fan type in -spaces with applications.
Minimax theorems without changeless proportion
The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some properties...
Minimax Theory with Transversal Points
Mixed semicontinuous perturbation of a second order nonconvex sweeping process.
Moduli and characteristics of monotonicity in some Banach lattices.
Monotone increasing multi-valued condensing random operators and random differential inclusions.
Monotone iterative technique and connectedness of the set of solutions
The paper deals with the properties of a monotone operator defined on a subset of an ordered Banach space. The structure of the set of fixed points between the minimal and maximal ones is described.
Multiple fixed points of positive mappings.
Multiple positive solutions for a second order delay boundary value problem on the half-line
Second order nonlinear delay differential equations are considered, and Krasnosel'skiĭ's fixed point theorem is used to establish a result on the existence of positive solutions of a boundary value problem on the half-line. This result can be used to guarantee the existence of multiple positive solutions. A specification of the result obtained to the case of second order nonlinear ordinary differential equations as well as to a particular case of second order nonlinear delay differential equations...
Multiple positive solutions of fourth-order impulsive differential equations with integral boundary conditions and one-dimensional -Laplacian.
Multiplicity results for sign-changing solutions of an operator equation in ordered Banach space
In this paper, we prove some multiplicity results for sign-changing solutions of an operator equation in an ordered Banach space. The methods to show the main results of the paper are to associate a fixed point index with a strict upper or lower solution. The results can be applied to a wide variety of boundary value problems to obtain multiplicity results for sign-changing solutions.