In this paper we present a theorem for defining fixed-points in categories of sheaves. This result gives a unifying and general account of most techniques used in computer science in order to ensure convergency of circular definitions, such as (but not limited to) well-founded recursion and contractivity in complete ultra metric spaces. This general fixed-point theorem encompasses also a simila...

The numerical solution of transferable differential-algebraic equations (DAE’s) by implicit Runge–Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is nonsingular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE’s with smooth solution we g...

Various results appear in the literature for deriving existence and uniqueness of fixed points for endofunctors on categories of complete metric spaces. All these results are proved for contracting functors which satisfy some further requirements, depending on the category in question. Following a new kind of approach, based on the notion of η-isometry, we show that the sole hypothesis of contr...

*Correspondence: [email protected] 1Department of Mathematics and Computer Sciences, Faculty of Natural Sciences, University of Gjirokastra, Gjirokastra, Albania Full list of author information is available at the end of the article Abstract In this paper, we introduce a new class of αqsp -admissible mappings and provide some fixed point theorems involving this class of mappings satisfying...

In this paper we present a new extension of coupled fixed point theorems in metric spaces endowed with a reflexive binary relation that is not necessarily neither transitive nor antisymmetric. The key feature in this coupled fixed point theorems is that the contractivity condition on the nonlinear map is only assumed to hold on elements that are comparable in the binary relation. Next on the ba...

Strong stability preserving (SSP) high order time discretizations were developed for solution of semi-discrete method of lines approximations of hyperbolic partial differential equations. These high order time discretization methods preserve the strong stability properties–in any norm or seminorm—of the spatial discretization coupled with first order Euler time stepping. This paper describes th...

Abstract We show that certain monotone functionals on the Hardy spaces and convex Bergman are maximized at normalized reproducing kernels among functions of norm 1, thus proving contractivity conjecture Pavlovi? Brevig, Ortega-Cerdà, Seip Zhao Wehrl-type entropy for SU (1, 1) group Lieb Solovej, respectively.