We provide some square-free criteria for primitive polynomials over unique factorization domains, which do not make use of derivatives or discriminants. Using some ideas of Ostrowski we establish nonvanishing conditions for determinants of matrices with polynomial entries and deduce squarefree criteria for polynomials in several variables.

Let G1 and G2 be disjoint copies of a graph G, and let f : V (G1) → V (G2) be a function. Then a functigraph C(G, f) = (V,E) has the vertex set V = V (G1) ∪ V (G2) and the edge set E = E(G1) ∪ E(G2) ∪ {uv | u ∈ V (G1), v ∈ V (G2), v = f(u)}. A functigraph is a generalization of a permutation graph (also known as a generalized prism) in the sense of Chartrand and Harary. In this paper, we study ...

Here we derive multivariate weighted fractional representation formulae involving ordinary partial derivatives of …rst order. Then we present related multivariate weighted fractional Ostrowski type inequalities with respect to uniform norm. 2010 AMS Mathematics Subject Classi…cation : 26A33, 26D10, 26D15.

a f (x) dx− b− a n n ∑ i=1 f (a+ xi (b− a)) ∣∣∣∣ 5 2m+ 5 4 (b− a)m+1 (m+ 1)! (S − s) (?) holds, where S := supa5x5b f (m)(x), s := infa5x5b f (m)(x) and for suitable x1, x2, . . . , xn. It is worth noticing that n,m are arbitrary numbers. This means that the estimate in (?) is more accurate whenm is large enough. Our approach is also elementary. © 2010 Elsevier Ltd. All rights reserved.

In this paper we present a historical review of the investigation of two Ostrowski inequalities and describe several distinct streams for their generalizations. Also we point out some new methods to obtain known results and give a number of new results related to Ostrowski’s inequalities.

The classical Ostrowski inequality for functions on intervals estimates the value of the function minus its average in terms of the maximum of its first derivative. This result is extended to higher order over shells and balls of R , N ≥ 1, with respect to an extended complete Tschebyshev system and the generalized radial derivatives of Widder type. We treat radial and non-radial functions.

Acknowledgment I want to give thanks to my mother, father, sisters and brothers for their permanent support, motivation, enthusiasm, and guidance on my life. I want to thank also to SENACYT and IFARHU who gave me the opportunity to study for an advanced degree in a prestigious international institution. I would also express my gratitude to Dr. Gerald J LaHoste for his professionalism, guidance ...

In this paper we present sharp estimates for the difference of general integral means with respect to even different finite measures. This is achieved by the use of the Ostrowski and Fink inequalities and the Geometric Moment Theory Method. The produced inequalities are with respect to the supnorm of a derivative of the involved function.