Multifunctions with selections of convex and concave type.
Multiple integrals evaluated by functional equations
Multiple Lebesgue integration on time scales.
Multiplication, distributivity and fuzzy-integral. I
The main purpose is the introduction of an integral which covers most of the recent integrals which use fuzzy measures instead of measures. Before we give our framework for a fuzzy integral we motivate and present in a first part structure- and representation theorems for generalized additions and generalized multiplications which are connected by a strong and a weak distributivity law, respectively.
Multiplication of fuzzy quantities
Multiplication of subharmonic functions.
Multiplicative concavity of the integral of multiplicatively concave functions.
Multiplicative functionals on algebras of differentiable functions.
Let Ω be an open subset of a real Banach space E and, for 1 ≤ m ≤, let Cm(Ω) denote the algebra of all m-times continuously Fréchet differentiable real functions defined on Ω. We are concerned here with the question as to wether every nonzero algebra homomorphism φ: Cm(Ω) → R is given by evaluation at some point of Ω, i.e., if there exists some a ∈ Ω such that φ(f) = f(a) for each f ∈ Cm(Ω). This problem has been considered in [1,4,5] and [6]. In [6], a positive answer is given in the case that...
Multiplicity and uniqueness for a class of discrete fractional boundary value problems
The paper deals with a class of discrete fractional boundary value problems. We construct the corresponding Green's function, analyse it in detail and establish several of its key properties. Then, by using the fixed point index theory, the existence of multiple positive solutions is obtained, and the uniqueness of the solution is proved by a new theorem on an ordered metric space established by M. Jleli, et al. (2012).
Multipliers for generalized Riemann integrals in the real line
We use an elementary method to prove that each function is a multiplier for the -integral.
Multipliers of spaces of derivatives
For subspaces, and , of the space, , of all derivatives denotes the set of all such that for all . Subspaces of are defined depending on a parameter . In Section 6, is determined for each of these subspaces and in Section 7, is found for and any of these subspaces. In Section 3, is determined for other spaces of functions on related to continuity and higher order differentiation.
Multipliers of the Fourier-Haar series.
Multiplying balls in the space of continuous functions on [0,1]
Let C denote the Banach space of real-valued continuous functions on [0,1]. Let Φ: C × C → C. If Φ ∈ +, min, max then Φ is an open mapping but the multiplication Φ = · is not open. For an open ball B(f,r) in C let B²(f,r) = B(f,r)·B(f,r). Then f² ∈ Int B²(f,r) for all r > 0 if and only if either f ≥ 0 on [0,1] or f ≤ 0 on [0,1]. Another result states that Int(B₁·B₂) ≠ ∅ for any two balls B₁ and B₂ in C. We also prove that if Φ ∈ +,·,min,max, then the set is residual whenever E is residual in...
Multistructures determined by differential rings
Multivalued mappings and Filippov's operation
Multivariate polynomial inequalities viapluripotential theory and subanalytic geometry methods
We give a state-of-the-art survey of investigations concerning multivariate polynomial inequalities. A satisfactory theory of such inequalities has been developed due to applications of both the Gabrielov-Hironaka-Łojasiewicz subanalytic geometry and pluripotential methods based on the complex Monge-Ampère operator. Such an approach permits one to study various inequalities for polynomials restricted not only to nice (nonpluripolar) compact subsets of ℝⁿ or ℂⁿ but also their versions for pieces...
Multivariate version of a Jensen-type inequality.