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Volume 7, No. 2, June 2014




Various Error Estimations for Several Newton–Cotes Quadrature Formulae in Terms of at Most First Derivative and Applications in Numerical Integration

Error estimates for midpoint, trapezoid, Simpson’s, Maclaurin’s, 3/8-Simpson’s and Boole’s type rules are obtained. Some related inequalities of Ostrowski’s type are pointed out. These results are obtained for mappings of bounded variation, Lipschitzian, and absolutely continuous mappings whose first derivatives are belong to Lp[a,b] (1p≤∞) Applications to numerical integration are provided.


M. W. Alomari

S. S. Dragomir


JJMS, 2014, 7(2), 89-108

Monotonic Analysis: Some Results of Increasing and Positively Homogeneous Functions

The theory of increasing and positively homogeneous (IPH) functions defined on a convex cone in a topological vector space X, is well developed. In this article, we present necessary and sufficient conditions for the minimum of the difference of strictly IPH functions defined on X. We study convergence of sequences of increasing positively homogeneous (IPH) functions defined on X.


H. Mazaheri

Z. Golinejad

JJMS, 2014, 7(2), 109-118


Related Monotonic Functions

We continue the study of related sets introduced by Prof. Min and generalize some of his results.


M. Sasirekha

JJMS, 2014, 7(2), 119-130

Central Idempotent of Rings

In this paper, we find several necessary conditions for the idempotents of a ring R to be central (for example: if eUR =UR e   for every idempotent e of R then the idempotents of R are central, where  UR is the set of units in R). We present some several properties of a ring whose idempotents are central (for instance: If IRÍCR then reg R = S.clR where reg R is the set of regular elements in R and S.cl is the set of strongly clean element in R).

Mohamed-Kheir Ahmad Sumyyah Al-Hijjawi

JJMS, 2014, 7(2), 131-145

Empirical Bayes Estimates of Rayleigh Distribution with Ewmel and Logarithmic Loss Functions for Censored Samples

In this paper, empirical Bayes estimates of reliability performances are derived when the data are progressively Type II censored from a Rayleigh distribution. These estimates are derived under exponentially weighted minimum expected loss (EWMEL) and logarithmic loss functions, and compared with the corresponding maximum likelihood estimates in terms of absolute bias and estimated risk. A real data set is presented to illustrate the proposed estimation method, and a Monte Carlo simulation study is carried out to investigate the accuracy of derived estimates. The study shows that the empirical Bayesian estimation outperforms the maximum likelihood estimation.


D. R. Barot

M. N. Patel


JJMS, 2014, 7(2), 147-170