Solution stability of a class of linear generalized equations in finite dimensional Euclidean spaces is investigated by means of generalized differentiation. Exact formulas for the Fréchet and the Mordukhovich coderivatives of the normal cone mappings of perturbed Euclidean balls are obtained. Necessary and sufficient conditions for the local Lipschitz-like property of the solution maps of such...

In [1], A. Branciari defines a Generalised metric space of finite order and establishes Banach contraction principle in it. The object of this paper is to extend this result to Quasi contraction and prove some fixed point results for two weakly compatible self maps satisfying a generalized contractive condition in this space without assuming it to be Hausdorff . Our result generalizes the said ...

We discuss about the generalized $F$-contraction mappings in partially ordered metric spaces. For this, we first introduce the notion of ordered weakly $F$-contraction mapping. We also present some fixed point results about this type of mapping in partially ordered metric spaces. Next, we introduce the notion of $acute{mathrm{C}}$iri$acute{mathrm{c}}$ type generalized ordered weakly $F$-contrac...

We study the exceptional loci of birational (bimeromorphic) contractions a hyperkähler manifold M. Such contraction locus is union all minimal rational curves in collection cohomology classes which are orthogonal to wall Kähler cone. Cohomology can possibly be cone some deformation M called MBM classes. prove that type (1,1) represented by curves, curves. Any curve contracted on an appropriate ...

For an n×n nonnegative matrix P , an isomorphism is obtained between the lattice of initial subsets (of {1, · · · , n}) for P and the lattice of P -invariant faces of the nonnegative orthant R+. Motivated by this isomorphism, we generalize some of the known combinatorial spectral results on a nonnegative matrix that are given in terms of its classes to results for a cone-preserving map on a pol...

In this paper, we first introduce the new notion of rational cyclic contraction and then establish some convergence theorems of best proximity points for two non-self mappings in the frame work of complete metric space. Our results generalized and improve some main results in the literature. An example is given to support our main results.

[Perov, A. I., On Cauchy problem for a system of ordinary diferential equations, (in Russian), Priblizhen. Metody Reshen. Difer. Uravn., 2 (1964), 115-134] used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article we study fixed point results for the new extensions of Banach’s contraction principle ...

The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $n which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function. In the following we show some results appeared in [2]. Definition 2.1 Let n1, . . . , np be posi...