In this note, we aim to present some properties of the space of all weakly fuzzy bounded linear operators, with the Bag and Samanta’s operator norm on Felbin’s-type fuzzy normed spaces. In particular, the completeness of this space is studied. By some counterexamples, it is shown that the inverse mapping theorem and the Banach-Steinhaus’s theorem, are not valid for this fuzzy setting. Also...

in this paper, a fuzzy version of the analytic form of hahn-banachextension theorem is given. as application, the hahn-banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.

In accordance with the Costa theorem, the interference which is independent of the channel input and known non-causally at the transmitter, does not affect the capacity of the Gaussian channel. In some applications, the known interference depends on the input and hence has some information. In this paper, we study the channel with input dependent interference and prove a capacity theorem that n...

The proposed theorem in this paper is indicative of a kind of duality in the propagation of waves in the dual media of and in the spherical structures. Independent of wave frequency, the number of layers, their thickness, and the type of polarization, this theorem holds true in case of any change in any of these conditions. Theorem: Consider a plane wave incident on a multilayered spheric...

The aim of this paper is to compute a simplicial cohomology group of some specific digital images. Then we define ringand algebra structures of a digital cohomology with the cup product. Finally, we prove a special case of the Borsuk-Ulam theorem fordigital images.

We give a characterization of the ”uniform closure” of the dual of a C-algebra. Some applications in harmonic analysis are given. 1. Four topologies on the unit ball of a C-algebra Let A be a C-algebra and P (A),S(A),A1, and A denote the pure state space, state space, closed dual unit ball, and the dual of A, respectively, all equipt with the w-topology. Let A1denote the closed unit ball of A. ...

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

in this paper we prove a unique common coupled fixed point theorem for two pairs of $w$-compatible mappings in $s_b$-metric spaces satisfying a contrctive type condition. we furnish an example to support our main theorem. we also give a corollary for junck type maps.