In the present paper, we first introduce different types of fuzzy continuity for mappings between F-normed linear spaces and relations them are investigated. Secondly, principles functional analysis established in context F-spaces. More precisely, based on fact that topological equivalent, obtain closed graph theorem open mapping theorem. Using Zabreiko’s lemma, prove uniform bounded principle ...

The nitely presented group G is hyperbolic ii H 2 (1) (G; ` 1) = 0. I have established the following result, full details for which will appear in a forthcoming paper. Theorem 1. The nitely presented group G is hyperbolic ii H 2 (1) (G; ` 1) = 0. For the deenition of thè 1-cohomology, see Ge1]. The coeecient group`1 here is the Banach space of bounded functions on a countably innnite set in the...

This paper addresses the Entropic Value-at-Risk (EV@R), a recently introduced coherent risk measure. It is demonstrated that the norms induced by EV@R induce the same Banach spaces, irrespective of the confidence level. Three spaces, called the primal, dual, and bidual entropic spaces, corresponding with EV@R are fully studied. It is shown that these spaces equipped with the norms induced by EV...

The main concern of this paper is to investigate the existence and uniqueness a fuzzy neutral impulsive stochastic differential system with Caputo fractional order driven by Brownian motion using numbers bounded ν-level intervals that are convex, normal upper-semicontinuous. Fuzzy Itô process, Grönwall’s inequality Banach fixed-point theorem employed probe local global existence. An analytical ...

We prove complex interpolation theorems for analytic families of multilinear operators defined on quasi-Banach spaces, with explicit constants on the intermediate spaces. We obtain analogous results for analytic families of operators defined on spaces generated by the Calderón method applied to couples of quasi-Banach lattices with nontrivial lattice convexity. As an application we derive a mul...

These notes give a summary of results that everyone who does work in functional analysis should know about the weak topology on locally convex topological vector spaces and the weak-* topology on their dual spaces. The most striking of the results we prove is Theorem 9, which shows that a subset of a locally convex space is bounded if and only if it is weakly bounded. It is straightforward to p...

We give an answer to the Problem 11.6 posed by Stephen Simons in his book ”From Hahn-Banach to Monotonicity”: Do there exist a nonzero finite dimensional Banach space and a pair of extended real-valued, proper and convex functions which is totally Fenchel unstable? The answer is negative.