In this paper we prove an analogue of Banach and Kannan fixed point theorems by generalizing the Lipschitz constat $k$, in generalized Lipschitz mapping on cone metric space over Banach algebra, which are answers for the open problems proposed by Sastry et al, [K. P. R. Sastry, G. A. Naidu, T. Bakeshie, Fixed point theorems in cone metric spaces with Banach algebra cones, Int. J. of Math. Sci. ...

The linear spaces generated by the eigenfunctions of a diierential operator are well-known in applied mathematics. In this paper we examine their interpolation properties, connection with Sobolev spaces and apply these results to the solving of hyperbolic equation in Sobolev spaces of fractional order. 1. Interpolation and function spaces Let A 1 and A 2 be two Banach spaces, linearly and conti...

We propose a notion of weak (n + k, n)-category, which we call (n + k, n)Θ-spaces. The (n + k, n)-Θ-spaces are precisely the fibrant objects of a certain model category structure on the category of presheaves of simplicial sets on Joyal’s category Θn. This notion is a generalization of that of complete Segal spaces (which are precisely the (∞, 1)-Θ-spaces). Our main result is that the above mod...

This note corrects an error in the char(K) = 2 case of the author’s computation of the bordism groups of K-Witt spaces for the field K. A complete computation is provided for the unoriented bordism group. For the oriented bordism groups, a nearly complete computation is provided as well a discussion of the difficulty of resolving a remaining ambiguity in dimensions equivalent to 2 mod 4. Recall...