The theory of (R, <,+,Z,Za) is decidable if a is quadratic. If a is the golden ratio, (R, <,+,Z,Za) defines multiplication by a. The results are established by using the Ostrowski numeration system based on the continued fraction expansion of a to define the above structures in monadic second order logic of one successor. The converse that (R, <,+,Z,Za) defines monadic second order logic of one...

Abstract The objective of this article is to incorporate the concept Ostrowski inequality with Atangana–Baleanu fractional integral operator. A novel identity for twice-differentiable functions established after a rigorous investigation several basic definitions and existing ideas related inequalities calculus. Following that, numerous Ostrowski-type are provided based on identity, which uses M...

We firstly establish an identity for $n$ time differentiable mappings Then, a new inequality for $n$ times differentiable functions is deduced. Finally, some perturbed Ostrowski type inequalities for functions whose $n$th derivatives are of bounded variation are obtained.

In this paper, a new general identity for differentiable mappings via Riemann-Liouville fractional integrals has been defined. By using of this identity, author has obtained new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for functions whose derivatives in absolutely value at certain powers are s-convex in the second sense.

Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this article, we establish some companions of an Ostrowski-like type inequality for functions whose second derivatives in absolute value are convex and concave.

Ostrowski established in 1919 that an absolutely irreducible integral polynomial remains absolutely irreducible modulo all sufficiently large prime numbers. We obtain a new lower bound for the size of such primes in terms of the number of integral points in the Newton polytope of the polynomial, significantly improving previous estimates for sparse polynomials.