The classical Mazur-Ulam theorem states that every surjective isometry between real normed spaces is affine. In this paper, we study 2-isometries in probabilistic 2-normed spaces....

}\\perp_R}\\). A linear mapping \\({U: \\mathcal{X} \\to \\mathcal{Y}}\\) between real normed spaces is called an \\({\\varepsilon}\\)-isometry if \\({(1 - \\varphi_1 (\\varepsilon))\\|x\\| \\leq \\|Ux\\| \\leq (1 + \\varphi_2(\\varepsilon))\\|x\\|\\,\\,(x \\in...

We investigate approximate partial isometries and approximate generalized inverses. We also prove that if T is an invertible contraction satisfying displaystyle{ | T T^{*} T - T | < epsilon < {2 over 3 sqrt{3}}}. Then there exists a...

The classical Mazur–Ulam theorem which states that every surjective isometry between real normed spaces is affine is not valid

for non-Archimedean normed spaces. In this paper, we establish a Mazur–Ulam theorem in the non-Archimedean strictly...

In this talk, we represent the recent results on the generalized

Hyers–Ulam–Rassias stability of functional equations and

the perturbation of isometries, homomorphisms and derivations in

various settings such as as classical...