R. Vasuki [1] proved fixed point theorems for expansive mappings in Menger spaces. R. Gujetiya and et al [2] presented an extension of the main result of Vasuki, for four expansive mappings in Menger space. In this article, an important lemma is given to prove that the iteration sequence is Cauchy under suitable condition in Menger probabilistic G-metric space (shortly, MPGM-space). And then, used to obtain three common fixed point theorems for expansive type mappings.

<p>In this paper, we prove there exists a coupled fixed point for a set- valued contraction mapping defined on X× X , where X is incomplete ordered G-metric. Also, we prove the existence of a unique fixed point for single valued mapping with respect to implicit condition defined on a complete G- metric.</p>

In this paper, new concepts which are called: left derivations and generalized left derivations in nearrings have been defined. Furthermore, the commutativity of the 3-prime near-ring which involves some
algebraic identities on generalized left derivation has been studied.

Chemical pollution is a very important issue that people suffer from and it often affects the nature of health of society and the future of the health of future generations. Consequently, it must be considered in order to discover suitable models and find descriptions to predict the performance of it in the forthcoming years. Chemical pollution data in Iraq take a great scope and manifold sources and kinds, which brands it as Big Data that need to be studied using novel statistical methods. The research object on using Proposed Nonparametric Procedure NP Method to develop an (OCMT) test procedure to estimate parameters of linear regression model with large size of data (Big Data) which comprises many indicators associated with chemi

The objective of this study was tointroduce a recursive least squares (RLS) parameter estimatorenhanced by using a neural network (NN) to facilitate the computing of a bit error rate (BER) (error reduction) during channels estimation of a multiple input-multiple output orthogonal frequency division multiplexing (MIMO-OFDM) system over a Rayleigh multipath fading channel.Recursive least square is an efficient approach to neural network training:first, the neural network estimator learns to adapt to the channel variations then it estimates the channel frequency response. Simulation results show that the proposed method has better performance compared to the conventional methods least square (LS) and the original RLS and it is more robust a

This research is concerned with the re-analysis of optical data (the imaginary part of the dielectric function as a function of photon energy E) of a-Si:H films prepared by Jackson et al. and Ferlauto et al. through using nonlinear regression fitting we estimated the optical energy gap and the deviation from the Tauc model by considering the parameter of energy photon-dependence of the momentum matrix element of the p as a free parameter by assuming that density of states distribution to be a square root function. It is observed for films prepared by Jackson et al. that the value of the parameter p for the photon energy range is is close to the value assumed by the Cody model and the optical gap energy is which is also close to the value

In this article we study the variance estimator for the normal distribution when the mean is un known depend of the cumulative function between unbiased estimator and Bays estimator for the variance of normal distribution which is used include Double Stage Shrunken estimator to obtain higher efficiency for the variance estimator of normal distribution when the mean is unknown by using small volume equal volume of two sample .