# Volume 3 (2011), Number 2

## On Some New Fejér-type Inequalities for Co-ordinated Convex Functions

### Author(s): M. A. LATIF, S. HUSSAIN AND S. S. DRAGOMIR

**Abstract:** In this paper some new mappings associated with the Fejér
inequality for double integrals are deﬁned and as a consequence some new Fejér
type inequalities for co-ordinated convex functions are established as well.

## Inequalities of Ostrowski and Simpson Type for Mappings of Two Variables with Bounded Variation and Applications

### Author(s): Y. JAWARNEH AND M.S.M. NOORANI

**Abstract:** In this paper two inequalities of Ostrowski type and Simpson
type for mappings of two independent variables with bounded variation are established.
General inequality of trapezoid type is obtained. Applications to some special
means and to a quadrature formula are given.

## Generalized Type of Entire Monogenic Functions of Slow Growth

### Author(s): SUSHEEL KUMAR AND KIRANDEEP BALA

**Abstract:** In the present paper we study the generalized growth of entire
monogenic functions having slow growth. The characterizations of generalized type
of entire monogenic functions have been obtained in terms of their Taylor’s
series coefficients.

## On the Best Polynomial Approximation of Generalized Biaxisymmetric Potentials in ${L}^{p}$-norm, $p\ge 1$

### Author(s): HUZOOR H. KHAN AND RIFAQAT ALI

**Abstract:** The real valued regular solution of generalized biaxially symmetric
potential equation $$\frac{{\partial}^{2}F}{\partial {x}^{2}}+\frac{{\partial}^{2}F}{\partial {y}^{2}}+\frac{\left(2\alpha +1\right)}{x}\frac{\partial F}{\partial x}+\frac{\left(2\beta +1\right)}{y}\frac{\partial F}{\partial y}=0,\alpha >\beta >-\frac{1}{2}$$ are called generalized biaxisymmetric
potentials. In this paper, the characterization of lower order and lower type of entire GBASP
$F$ in term
of their approximation error ${E}_{n}^{p}\left({F}_{\sigma}\right)$ in ${L}^{p}$-norm,
$p\ge 1$ have been obtained. The analysis utilizes the Bergman and Gilbert Integral
Operator Method to extend results from classical function theory on the best polynomial
approximation of analytic functions of one complex variable.

## On $q$-Hahn’s Theorem: a $q$-extension

### Author(s): L. KHÉRIJI AND P. MARONI

**Abstract:** We give a $q$-analogue of Hahn’s theorem and a $q$-extension for it; we show that an orthogonal polynomial
sequence, whose $m-th$ associated sequence of
$k-th$ $q$-derivative sequence is orthogonal, is necessarily a
${H}_{q}$-classical one, where ${H}_{q}$ is the
$q$
-difference operator.

## The Direct and the Inverse Problem for Simple Regression Models

### Author(s): FELICIA ZĂVOIANU AND CONSTANTIN ZĂVOIANU

**Abstract:** This article contains a personal point of view regarding the
implementation of simple regression models. We consider that the approach of
considering in parallel both the direct and inverse problems helps in constructing
a global, in depth, image regarding the usefulness of simple regression problems.

## Study of Improvement of Rotation Mechanism Ball of EsRc-1400 Rotor Excavator

### Author(s): VILHELM ITU, IOSIF DUMITRESCU AND DUMITRU JULA

**Abstract:** The paper presents the study of the possibility of improvement
of EsRc-1400 rotor excavator’s rotation mechanism ball.

## Veriﬁcation by Analytical Calculus of the Winding Pulley Shaft of Lonea Mining Plant New Shaft with Skip

### Author(s): IOSIF DUMITRESCU, VILHELM ITU AND MIHAI CARMELO RIDZI

**Abstract:** The pulley mounted in the tower at the winding installation
with the entailing part of the winding cable on the soil, are winding pulleys.
The winding pulleys are auxiliary installation devices with the role of supporting
and guiding the winding cable on the vertical symmetry axis of the winding shaft.
The pulley unit is made up of the pulley shaft and its bearings by which the unit is
fixed to the winding tower structure, the mobile pulley and fixed pulley are mounted
to the pulley shaft. The paper presents the verification calculus of the Lonea type
winding shaft pulley for Lonea Mining Plant with new skip with analytical method.