The approxımatıon propertıes of q − generalızatıons of some lınear posıtıve operator sequences

Korovkin tipli yaklaşım teoremleri yaklaşımlar teorisinde önemli bir yere sahiptir. İstatistiksel yakınsaklık kavramı yardımıyla Korovkin tipli yaklaşım teoremleri geliştirilmiştir [Gadjiev ve Orhan, 2002; Duman ve ark. 2003]. Bu teoremler kullanılarak birçok lineer pozitif operatörün q − genelleşmelerinin veya integral tipli genelleşmelerinin yaklaşım özellikleri araştırılabilmiştir. Bu tezde ise, Aral ve Gupta (2006) tarafından tanımlanan q − Szasz-Mirakjan operatörlerinin Kantorovich tipli genelleşmesi verilmiş ve istatistiksel yaklaşım özellikleri incelenmiştir. Yaklaşım teorisinde operatörlerin düzgün yakınsaklığının araştırılması kadar bu yakınsamanın hızının değerlendirilmesi de oldukça önemli bir konudur. Bu tezde, ilk olarak oluşturulan operatörler dizisi için Voronovskaja tipli teorem bu yüzden verilmiştir. Daha sonra süreklilik modülü yardımıyla istatistiksel yaklaşım hızı elde edebilmek için q − Szasz-Mirakjan operatörlerinin yeni bir Kantorovich tipli genelleşmesi oluşturulmuştur. Ayrıca pozitif bir operatör olan Riemann tipli q − integral yardımıyla q − Szasz-Mirakjan-Kantorovich operatörleri geliştirilip ağırlıklı süreklilik modülü yardımıyla yaklaşım oranı elde edilmiştir. Bunun yanında Riemann tipli q − integral yardımıyla oluşturulan operatörlerin iki değişkenli genelleşmesinin istatistiksel yaklaşım özellikleri de verilmiştir. Yukarıda sözü edilen operatörlerin q = 1 olması durumunda klasik operatörlerin integral tipli genelleşmelerine dönüşmesi ve q yerine ( ) n q dizisi alınarak bu dizinin seçimine göre yaklaşım hızının uygun şekilde ayarlanabilir olması tezin önemini artırmaktadır.Korovkin type approximation theorems have fundamental role in the approximation theory. By the aid of the concept of statistical approximation, Korovkin type theorems are developed [Gadjiev and Orhan, 2002; Duman et all, 2003]. Using these theorems, the approximation properties of the q − generalizations and integral-type generalizations of many linear positive operators can be investigated. In this thesis, Kantorovich-type generalization of q − Szasz-Mirakjan operators defined by Aral and Gupta (2006) is given and statistical approximation properties of this generalization are investigated. In the approximation theory, evaluation of approximation rate is as important subject as an investigation of uniform convergence of operators. Hence, Voronovskaja type theorem is given for constructed operators' sequence in this thesis. Then, a new Kantorovich type generalization of the q − Szasz-Mirakjan operators is defined to obtain statistical approximation rate by means of modulus of continuity. Furthermore, q − Szasz-Mirakjan-Kantorovich operators are developed with the aid of Riemann type q − integral and the approximation rate is obtained by the weighted modulus of continuity. Also, statistical approximation properties of two variable generalizations of operators constructed by the Riemann type q − integral are given. In the case of q = 1 , since our operators are reduced to the integral type generalization of the classical operators, and since the approximation rate can properly be calibrated by a proper choose of ( ) n q instead of q , increase the importance of this thesis

An optimistic-pessimistic DEA model based on game cross efficiency approach

The ranking of the decision making units (DMUs) is an essential problem in data envelopment analysis (DEA). Numerous approaches have been proposed for fully ranking of units. Majority of these methods consider DMUs with optimistic approach, whereas their weaknesses are ignored. In this study, for fully ranking of the units, a modified optimistic–pessimistic approach, which is based on game cross efficiency idea is proposed. The proposed game like iterative optimistic-pessimistic DEA procedure calculates the efficiency scores according to weaknesses and strengths of units and is based on non-cooperative game. This study extends the optimistic-pessimistic DEA approach to obtain robust rank values for DMUs. The proposed approach yields Nash equilibrium solution, thus overcomes the problem of non-uniqueness of the DEA optimal weights that can possibly reduce the usefulness of cross efficiency. Finally, in order to verify the validity of the proposed model and to show the practicability of algorithm, we apply a real-world example for selection of industrial R&D projects. The proposed model can increase the discriminating power of DMUs and can fully rank the DMUs

A new approach based on regression analysis and mathematical programming to multi-group classification problems

WOS: 000472481600019In this study, for solving multi-group classification problems, a new two-stage hybrid classification method based on regression analysis and mathematical programming has been developed. In the first step of the proposed method, the classification score of each unit is estimated with the help of the linear regression equation for each unit. In the second step, the classification of the units is performed by the mathematical programming model based on clustering analysis. The proposed method combines the strengths of regression analysis and mathematical programming method. From the 10 real data sets taken the well-known literature and simulation study results, it is observed that the proposed method outperforms the regression analysis, mathematical programming and artificial neural network based classification methods

Approximation properties of modified Szász-Mirakyan operators in polynomial weighted space

Abstract: We introduce certain modified Szász-Mirakyan operators in polynomial weighted spaces of functions of one variable. We studied approximation properties of these operators