The theory of iterated function systems (IFSs) has been an active area research on fractals and various types self-similarity in nature. basic theoretical work IFSs proposed by Hutchinson. In this paper, we introduce a new generalization Hutchinson IFS, namely generalized ?-contraction which is finite collection functions T1,…,TN from Cartesian product space X×?×X into X, where (X,d) complete m...

Lie bialgebra contractions are introduced and classified. A non-degenerate coboundary bialgebra structure is implemented into all pseudo-orthogonal algebras so(p, q) starting from the one corresponding to so(N +1). It allows to introduce a set of Lie bialgebra contractions which leads to Lie bialgebras of quasi-orthogonal algebras. This construction is explicitly given for the cases N = 2, 3, 4...

We propose residual based tests for cointegration using local GLS detrending (Elliott, Rothemberg and Stock, 1996, ERS) applied separately to each variable of the system. We consider two cases, one where only a constant is included and one where a constant and a time trend are included. We derive the asymptotic distribution of a feasible point optimal test which allows us to derive the power en...

In this paper, we introduce and study a class of generalized nonlinear vector quasi-variationallike inequalities with set-valued mappings in Hausdorff topological vector spaces which includes generalized nonlinear mixed variational-like inequalities, generalized vector quasi-variational-like inequalities, generalizedmixed quasi-variational-like inequalities and so on. Bymeans of fixed point the...

In this paper, we introduce and study the system of generalized vector quasi-variational-like inequalities in Hausdorff topological vector spaces. By means of fixed point theorem, we obtain existence theorem for the system of generalized vector quasi-variational-like inequalities and also derive the existence result of solutions for the generalized vector quasi-variational-like inequalities. Ke...