Download Hermite-Hadamard inequality in the geometry of Banach spaces by Kikianty E. PDF
By Kikianty E.
Read or Download Hermite-Hadamard inequality in the geometry of Banach spaces PDF
Similar geometry books
Conceptual Spaces: The Geometry of Thought
Inside of cognitive technology, methods at present dominate the matter of modeling representations. The symbolic procedure perspectives cognition as computation regarding symbolic manipulation. Connectionism, a unique case of associationism, versions institutions utilizing synthetic neuron networks. Peter Gardenfors bargains his concept of conceptual representations as a bridge among the symbolic and connectionist techniques.
There's an basically “tinker-toy” version of a trivial package over the classical Teichmüller house of a punctured floor, known as the embellished Teichmüller house, the place the fiber over some extent is the distance of all tuples of horocycles, one approximately each one puncture. This version ends up in an extension of the classical mapping classification teams referred to as the Ptolemy groupoids and to yes matrix types fixing similar enumerative difficulties, each one of which has proved priceless either in arithmetic and in theoretical physics.
The Lin-Ni's problem for mean convex domains
The authors end up a few subtle asymptotic estimates for optimistic blow-up suggestions to $\Delta u+\epsilon u=n(n-2)u^{\frac{n+2}{n-2}}$ on $\Omega$, $\partial_\nu u=0$ on $\partial\Omega$, $\Omega$ being a soft bounded area of $\mathbb{R}^n$, $n\geq 3$. particularly, they express that focus can ensue purely on boundary issues with nonpositive suggest curvature while $n=3$ or $n\geq 7$.
- Matrix Information Geometry
- Century of Geometry, 1830-1930: Epistemology, History, and Mathematics
- Geometry and Robotics: Workshop, Toulouse, France, May 26–28, 1988 Proceedings
- Elliptic theory on singular manifolds
- The Geometric Viewpoint: A Survey of Geometries
- Discrete and Computational Geometry and Graphs: 18th Japan Conference, JCDCGG 2015, Kyoto, Japan, September 14-16, 2015, Revised Selected Papers
Extra resources for Hermite-Hadamard inequality in the geometry of Banach spaces
Sample text
1. Let 1 < p < ∞. The space Lp ([0, 1], X) is a smooth (Fr´echet smooth) Banach space whenever X is smooth (Fr´echet smooth, respectively). We refer to McShane [84, p. 1. 2. Let 1 < p < ∞. The space Lp ([0, 1], X) is a reflexive Banach space if X is reflexive. Bochner in [13, p. 930] stated that if X and its dual X∗ are of (D)-property (namely, any function of bounded variation is differentiable almost everywhere [13, p. 914–915]) and X is reflexive, then Lp ([0, 1], X) is reflexive. However, further studies have shown that these conditions could be reduced to a simpler condition.
The p-th power mean of f on [a, b], which is defined by [p] M[a,b] (f ) = 1 b−a 1 p b p f (x) dx , a [r] [s] is increasing on R, that is, if −∞ ≤ r < s ≤ ∞, then, M[a,b] (f ) ≤ M[a,b] (f ). 5, we obtain the following consequence. 6 (Kikianty and Dragomir [71]). The p-HH-norm is monotonically increasing as a function of p on [1, ∞], that is, for any 1 ≤ r < s ≤ ∞ and (x, y) ∈ X2 , we have (x, y) r−HH ≤ (x, y) s−HH . Proof. Consider the nonnegative function f (t) = (1 − t)x + ty on [0, 1]. 3), we conclude that f ∈ Lp [0, 1] for 1 ≤ p ≤ ∞.
X, λy] = λ[x, y] for all x, y ∈ X and λ a scalar in K and λ is the conjugate of λ. A vector space equipped with a semi-inner product is called a semi-inner product space. According to Lumer [54], the importance of this concept is that every normed space can be represented as a semi-inner product space, so that the theory of operators on Banach spaces may be penetrated by Hilbert spaces type arguments. As it has more general axioms, obviously there are some limitations on the theory of semi-inner product spaces in comparison to that of Hilbert spaces [54].