in this paper the bagley-torvik equation as a prototype fractional differential equation with two derivatives is investigated by means of homotopy perturbation method. the results reveal that the present method is very effective and accurate.

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, 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.

The Baire theory of category, which classifies sets into two distinct categories, is an important topic in the study of metric spaces. Many results in topology arise from category theory; in particular, the Baire categories are related to a topological property. Because the Baire Category Theorem involves nowhere dense sets in a complete metric space, this paper first develops the concepts of n...

We generalize the Baire Category Theorem to the Borel and difference hierarchies, i.e. if Γ is any of the classes Σξ , Π 0 ξ , Dη(Σ 0 ξ) or Ďη(Σ 0 ξ) we find a representative set PΓ ∈ Γ and a Polish topology τΓ such that for every A ∈ Γ̌ from some assumption on the size of A ∩ PΓ we can deduce that A \ PΓ is of second category in the topology τΓ. This allows us to distinguish the levels of the B...

Let T be a topological structure and let A be a subset of the carrier of T . Then IntA is a subset of T . Let T be a topological structure and let P be a subset of the carrier of T . Let us observe that P is closed if and only if: (Def. 1) −P is open. Let T be a non empty topological space and let F be a family of subsets of T . We say that F is dense if and only if: (Def. 2) For every subset X...

In a recent paper E. J. McShane [3]2 has given a theorem which is the common core of a variety of results about Baire sets, Baire functions, and convex sets in topological spaces including groups and linear spaces. In general terms his theorem states that if J is a family of open maps defined in one topological space Xi into another, X2, the total image JiS) of a second category Baire set S in ...