In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...

function, 51 Riemann integral, 51 adjoint bilinear form, 65 almost separably valued, 53 Ascoli Theorem, 8 Banach space reflexive, 6 separable, 2 Banach-Steinhaus Theorem, 5 Bessel’s inequality, 9 biharmonic, 61 bilinear form, 55, 58 bounded, 58 strongly positive, 58 Bochner-Pettis Theorem Theorem, 53 Bounded Inverse Theorem, 6 Calculus in W 1,p(I;X) Theorem, 54 Campanato ’63 Theorem, 86 Campana...

A generalization of the Flow-box Theorem is proven. The assumption of a C vector field f is relaxed to the condition that f be locally Lipschitz. The theorem holds in any Banach space.

We prove analogs of Thom’s transversality theorem and Whitney’s theorem on immersions for pseudo-holomorphic discs. We also prove that pseudo-holomorphic discs form a Banach manifold. MSC: 32H02, 53C15.

We study model theoretical stability for structures from functional analysis. We prove a functional-analytic version of the Finite Equivalence Relation Theorem. We also the Stability Spectrum Theorem for Banach space structures.