Add to ORKGAbstract. Some properties of isometric mappings as well as approximate isometries are studied. 2000 Mathematics Subject Classification. Primary 46B04. 1. Isometry and linearity. Mazur and Ulam [17] proved the following well-known result concerning isometries, that is, transformations which preserve distances. Theorem 1.1. Given two real normed vector spaces X and Y, let U be a surjective mapping from X onto Y such that ‖U(x)−U(y) ‖ = ‖x−y ‖ for all x and y in X. Then the mapping xU(x)−U(0) is linear. Since continuity is implied by isometry, the proof of this theorem consists of show-ing that U(x)−U(0) is additive, and the additivity of this mapping will follow if we can prove that U satisfies Jensen’s equation:
In this article, we prove that any surjective isometry between unit spheres of $\ell^{\infty}$-sum o...
AbstractIn this paper, we will study the isometric extension problem for L1-spaces and prove that ev...
We prove that if a one-to-one mapping f: R3 → R3 preserves regular dodecahedrons, then f is a linear...
Abstract. Some properties of isometric mappings as well as approximate isometries are studied. 2000 ...
AbstractSome relations between isometry and linearity are examined. In particular, generalizations o...
This paper contains an exposition of two theorems on Banach spaces. Let X and Y be real Banach space...
We prove that if a one-to-one mapping f: Rn → Rn (n ≥ 2) preserves the unit circles, then f is a lin...
Abstract. Let X and Y be normed linear spaces. A mapping T: X → Y is called preserving the distance ...
ABSTRACT. Let X and Y be real Banach spaces. A mapping q5: X--t Y is called an &-isometry if 1 I...
In this paper, we study the extension of isometries between the unit spheres of L∞ and a normed...
International audienceGiven two normed spaces $X$ , $Y$ , the aim of this paper is establish that th...
Beckman, F.S and Quarles D.A, have proven in [1], the following theorem: Each function from the d-Eu...
We will prove that if a one-to-one mapping f: R3 → R3 preserves regular hexahedrons, then f is a lin...
We will prove that if a one-to-one mapping f:ℝ3→ℝ3 preserves regular hexahedrons, then f is a linear...
AbstractThis paper contains several generalizations of the Mazur–Ulam isometric theorem in F*-spaces...
In this article, we prove that any surjective isometry between unit spheres of $\ell^{\infty}$-sum o...
AbstractIn this paper, we will study the isometric extension problem for L1-spaces and prove that ev...
We prove that if a one-to-one mapping f: R3 → R3 preserves regular dodecahedrons, then f is a linear...
Abstract. Some properties of isometric mappings as well as approximate isometries are studied. 2000 ...
AbstractSome relations between isometry and linearity are examined. In particular, generalizations o...
This paper contains an exposition of two theorems on Banach spaces. Let X and Y be real Banach space...
We prove that if a one-to-one mapping f: Rn → Rn (n ≥ 2) preserves the unit circles, then f is a lin...
Abstract. Let X and Y be normed linear spaces. A mapping T: X → Y is called preserving the distance ...
ABSTRACT. Let X and Y be real Banach spaces. A mapping q5: X--t Y is called an &-isometry if 1 I...
In this paper, we study the extension of isometries between the unit spheres of L∞ and a normed...
International audienceGiven two normed spaces $X$ , $Y$ , the aim of this paper is establish that th...
Beckman, F.S and Quarles D.A, have proven in [1], the following theorem: Each function from the d-Eu...
We will prove that if a one-to-one mapping f: R3 → R3 preserves regular hexahedrons, then f is a lin...
We will prove that if a one-to-one mapping f:ℝ3→ℝ3 preserves regular hexahedrons, then f is a linear...
AbstractThis paper contains several generalizations of the Mazur–Ulam isometric theorem in F*-spaces...
In this article, we prove that any surjective isometry between unit spheres of $\ell^{\infty}$-sum o...
AbstractIn this paper, we will study the isometric extension problem for L1-spaces and prove that ev...
We prove that if a one-to-one mapping f: R3 → R3 preserves regular dodecahedrons, then f is a linear...