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    A Korovkin type approximation theorem in statistical sense
    (Akademiai Kiado, 2006) Erkus, Esra; Duman, Oktay
    In this study, using the concept of A-statistical convergence we investigate a Korovkin type approximation result for a sequence of positive linear operators defined on the space of all continuous real valued functions on any compact subset of the real m-dimensional space.
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    Families of linear generating functions for polynomials in two variables
    (Taylor & Francis Ltd, 2006) Altin, Abdullah; Erkus, Esra; Oezarslan, Mehmet Ali
    In the present paper, we derive various families of linear, mixed multilateral and multilinear generating functions for a class of polynomials in two variables. Some further results of the above types are also discussed.
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    Speciative determination of Cr(III) and Cr(VI) in dyeing waste water of Dil Creek discharge to Izmit Gulf (Izmit-Kocaeli, Turkey) by ICP-AES
    (Springer, 2008) Oktor, Kadriye; Yilmaz, Selehattin; Tuerker, Guelen; Erkus, Esra
    Wastewater pollution in industrial areas is one of the most important environmental problems. Heavy metal pollution, especially chromium pollution in wastewater sources from dyeing and tannery has affected the life on earth. This pollution can affect all ecosystems and human health directly or by food chain. Therefore, the determination of chromium in this study is of great importance. Dil Creek is located in the eastern Marmara region and discharges into the Izmit Gulf. This water source is used for irrigation in agriculture and as drinking water for animals. In this study, a rapid, sensitive and selective method for the speciative direct determination of Cr (III) and Cr (VI) in dyeing waste water samples collected from the nearest station to Izmit Gulf of Dil Creek in May 2006 by inductively coupled plasma-atomic emission spectrometry (ICP-AES) has been developed. An analysis of a given sample is completed in about 15 min for ICP-AES the method. As the result of the chromium analysis, the limit of quantification (LOQ) for the Cr (III), Cr (VI) and total Cr were founded as 0.0111 +/- 0.0002 mg/l (RSD, 1.80%), 0.0592 +/- 0.0010 mg/l (RSD, 1.70%) and 0.0703 +/- 0.0020 mg/l (RSD, 2.84%) respectively. In addition, the general mathematical formula has been developed to calculate the concentration of Cr(III), which can be applied to any other metal species. The result of Cr (VI) analysis indicated that water quality of Creek was IV. class quality according to the inland water classification. In order to validate the applied method, recovery studies were performed.
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    Statistical approximation of certain positive linear operators constructed by means of the Chan-Chyan-Srivastava polynomials
    (Elsevier Science Inc, 2006) Erkus, Esra; Duman, Oktay; Srivastava, H. M.
    In this study, by obtaining some Korovkin type approximation results in statistical sense for certain positive linear operators constructed by means of the Chan-Chyan-Srivastava multivariable polynomials [W.-C.C. Chan, C.-J. Chyan, H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transform. Spec. Funct. 12 (2001) 139-148], we show that our approximation method is stronger than the corresponding classical aspects in the approximation theory settings. Furthermore, we investigate their statistical rates by means of the modulus of continuity and the elements of the Lipschitz class. (c) 2006 Elsevier Inc. All rights reserved.
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    Statistical rates on the multivariate approximation theory
    (Pergamon-Elsevier Science Ltd, 2006) Duman, Oktay; Erkus, Esra; Gupta, Vijay
    Statistical rates of approximations by means of positive linear operators defined on the space of multivariate continuous functions are studied. Furthermore, displaying an example, it is shown that our statistical rates are more efficient than the classical aspects in the approximation theory. (c) 2006 Elsevier Ltd. All rights reserved.
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    The q-Lagrange polynomials in several variables
    (Mathematical Soc Rep China, 2006) Altin, Abdullah; Erkus, Esra; Tasdelen, Fatma
    Recently, Chan, Chyan and Srivastava [1] introduced and systematically investigated the Lagrange polynomials in several variables. The main object of this paper is to study a basic (or q-) analogue of the Chan-Chyan-Srivastava multivariable polynomials, which we define here. Several results involving generating functions are presented in this paper for the multivariable q-Lagrange polynomials.