We show that an analogue of the domain-theoretic least fixpoint operator can be defined in a purely set-theoretic framework. It can be formalized in classical higher order logic, serving as a solid foundation for proving termination of (possibly nested) recursive programs in a variety of mechanized proof systems.

Our theorems are on ordered cone metric spaces which are not necessarily normal. In the end, we describe the application of the main results in the integral equation.Although Du in [W‎. ‎S‎. ‎Du‎, ‎A note on cone metric fixed point theory and its equivalence‎, ‎Nonlinear Analysis‎, ‎72(2010) 2259-2261.]‎, ‎showed that the fixed point results in the setting of cone...

We investigate a steady flow of a viscous compressible fluid with inflow boundary condition on the density and inhomogeneous slip boundary conditions on the velocity in a cylindrical domain Ω = Ω0 × (0, L) ∈ R. We show existence of a solution (v, ρ) ∈ W 2 p (Ω) × W 1 p (Ω), where v is the velocity of the fluid and ρ is the density, that is a small perturbation of a constant flow (v̄ ≡ [1, 0, 0],...

I review the field-theoretic renomalization group approach to quantum gravity, built around the existence of a non-trivial ultraviolet fixed point in four dimensions. I discuss the implications of such a fixed point, found in three largely unrelated non-perturbative approaches, and how it relates to the vacuum state of quantum gravity, and specifically to the running of G. One distinctive featu...

In “zero-parameter” or classical Nielsen fixed point theory one studies Fix(f) := {x ∈ X | f(x) = x} where f : X → X is a map. In case X is an oriented compact manifold and f is transverse to the identity map, idX , Fix(f) is a finite set each of whose elements carries a natural sign, ±1, the index of that fixed point. The set Fix(f) is partitioned into Nielsen classes. Adding the indices withi...

We give an axiomatic treatment of fixed-point operators in categories. A notion of iteration operator is defined, embodying the equational properties of iteration theories. We prove a general completeness theorem for iteration operators, relying on a new, purely syntactic characterisation of the free iteration theory. We then show how iteration operators arise in axiomatic domain theory. One re...

We study singular discrete nth order boundary value problems with mixed boundary conditions. We prove the existence of a positive solution by means of the lower and upper solutions method and the Brouwer fixed point theorem in conjunction with perturbation methods to approximate regular problems. AMS subject classification: 39A10, 34B16.

in this paper, a concept of generalized weakly contraction mappings in partially ordered fuzzy metric spaces is introduced and  coincidence point  theorems on partially ordered fuzzy metric spaces are proved. also, as the corollary of these theorems, some common fixed point theorems on partially ordered fuzzy metric spaces are presented.