Mircea Ivan | Technical University of Cluj-Napoca (original) (raw)

Papers by Mircea Ivan

Bulletin of the Australian Mathematical Society, 2007

Some inequalities involving the binomial coefficients are obtained. They are used to determine th... more Some inequalities involving the binomial coefficients are obtained. They are used to determine the domain of convergence of the Bleimann, Butzer and Hahn approximation process for exponential type functions. An answer to Hermann's conjecture related to the Bleimann, Butzer and Hahn operators for monotone functions is given.

In the present paper we introduce Baskakov-Kantorovich-Bézier operators and study their rate of c... more In the present paper we introduce Baskakov-Kantorovich-Bézier operators and study their rate of convergence for functions of bounded variation. MSC 2000. 41A36, 41A25, 26A45.

Miskolc Mathematical Notes, 2018

We establish some mean value theorems involving n-simple functionals in the sense of Popoviciu. I... more We establish some mean value theorems involving n-simple functionals in the sense of Popoviciu. In particular, we obtain the Kowalewski mean value formula.

Publications de l'Institut Mathematique, 2015

We obtain a new recurrence formula for sequences of divided differences. In a particular case, th... more We obtain a new recurrence formula for sequences of divided differences. In a particular case, the recurrence formula simplifies the classical Newton-Girard identities relating power sums and elementary symmetric polynomials.

Journal of Mathematical Analysis and Applications, 2010

In this note we study the limit behavior of the iterates of a large class of positive linear oper... more In this note we study the limit behavior of the iterates of a large class of positive linear operators preserving the affine functions and, as a byproduct of our result, we obtain the limit of the iterates of Meyer-König and Zeller operators.

Journal of Mathematical Analysis and Applications, 2012

Journal of Mathematical Analysis and Applications, 2013

ABSTRACT We provide a highly convergent version of the generalized Euler sequence and we determin... more ABSTRACT We provide a highly convergent version of the generalized Euler sequence and we determine the element with the optimal rate of convergence in several classes of sequences of a prescribed form.The new approach extends and unifies many previous efforts in this direction. In addition, we answer an open problem on the asymptotic expansion of the Harmonic number sequence.

Journal of Approximation Theory, 2010

We generalize a recent result of de la Cal and Cárcamo concerning an extremal property of Bernste... more We generalize a recent result of de la Cal and Cárcamo concerning an extremal property of Bernstein operators.

Journal of Approximation Theory, 2011

We have devised a new method for the study of the asymptotic behavior of the iterates of positive... more We have devised a new method for the study of the asymptotic behavior of the iterates of positive linear operators. This technique enlarges the class of operators for which the limit of the iterates can be computed. c

Applied Mathematics Letters, 2010

Let n be an integer, n > 1. Theorem. If A : C[a, b] → R is a continuous linear functional orthogo... more Let n be an integer, n > 1. Theorem. If A : C[a, b] → R is a continuous linear functional orthogonal to all polynomials of degree at most n − 1, then the the inequalities A 2 (f) ≤ (−1) k (2k − 1)! A s A t (t − s) 2k−1 + f (k) 2 2 , are satisfied for all f ∈ C n [a, b] and k = 2,. .. , n. The previous theorem generalizes results contained in the following papers:

Applied Mathematics Letters, 2011

In this note we introduce a simple and efficient technique for studying the asymptotic behavior o... more In this note we introduce a simple and efficient technique for studying the asymptotic behavior of the iterates of a large class of positive linear operators preserving constant functions.

Abstract and Applied Analysis, 2011

We present a general result concerning the limit of the iterates of positive linear operators act... more We present a general result concerning the limit of the iterates of positive linear operators acting on continuous functions defined on a compact set. As applications, we deduce the asymptotic behaviour of the iterates of almost all classic and new positive linear operators.

Journal of Approximation Theory, 2009

Bleimann-Butzer-Hahn operators L n. Our main result states that for each locally bounded positive... more Bleimann-Butzer-Hahn operators L n. Our main result states that for each locally bounded positive function h there exists a continuous positive function f defined on [0, ∞) with L n f → f (n → ∞), pointwise on [0, ∞), such that lim sup x→+∞ f (x) h(x) = +∞. Moreover we construct an explicit counterexample function to Hermann's conjecture.

Journal of Mathematical Analysis and Applications, 2007

The complete asymptotic expansion of power means in terms of Bell polynomials is obtained. Some r... more The complete asymptotic expansion of power means in terms of Bell polynomials is obtained. Some results recently obtained by M. Bjelica are generalized.

Czechoslovak Mathematical Journal, 2010

Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents ... more Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.