A function is called arc-analytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arc-analytic functions that are not real analytic. Arc analytic functions appear while studying the arc-symmetric sets and the blow-analytic equivalence. In this paper we show that the non-analyticity locus of an arc-analytic function is arc-symmetric. We disc...

where σ is the Lipschitz constant of the extension of f and P is the natural probability on {0, 1}. Here we extend this inequality to more general product probability spaces; in particular, we prove the same inequality for {0, 1} with the product measure ((1− η)δ0 + ηδ1) . We believe this should be useful in proofs involving random selections. As an illustration of possible applications we give...

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 Algebraic Geometry smooth varieties are (in general) well-understood. By contrast (or simply because of that) the objects of interest are often singular varieties. From the theoretical point of view a remedy for this situation is the famous Theorem of Hironaka [8] on the resolution of singularities: If X is a variety over a field of characteristic 0 then there always exists a smooth variety ...

a famous theorem of schur states that for a group $g$ finiteness of $g/z(g)$‎ ‎implies the finiteness of $g'.$ the converse of schur's theorem is an interesting problem which has been considered by some‎ ‎authors‎. ‎recently‎, ‎podoski and szegedy proved the truth of the converse of schur's theorem for capable groups‎. ‎they also established an explicit bound for the index of the...

Boujari [5] proved a fixed point theorem with an old version of the integraltype contraction , his proof is incorrect. In this paper, a new generalizationof integral type contraction is introduced. Moreover, a fixed point theorem isobtained.

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

in this paper is introduced a new type of generalization of metric spaces called sb metric space. for this new kind of spaces it has been proved a common xed point theorem for four mappings which satisfy generalized contractive condition. we also present example to conrm our theorem.