Mediha Örkcü

This article investigates combining traditional methods for solving differential equations with Aboodh integral transformation and the Bernstein method. This approach offers a new perspective in solving various differential and integral equations. The solution approach obtained from the combination of Bernstein polynomials and integral transformations stands out in terms of theoretical and practical implications. This method can be applied to various examples of differential equations, and its practical applicability can be evaluated through studies conducted using programming languages. The error between the exact solution and the proposed method’s approximate solution has been calculated. We compare the numerical results of the Aboodh-Bernstein, Laplace-Bernstein, and Sumudu-Bernstein methods.

In the present paper, our purpose is to generalize the Jakimovski-Leviatan-Păltănea operators in the sense of Chlodowsky. After introducing the new operators we first obtain the moments of these operators in order to establish the convergency properties with the help of Korovkin's theorem. After that, we give the local approximation result and the Voronovskaya type theorem. We also examine the convergence properties of the operators in the weighted space of functions. Lastly we determine the rate of convergence of the operators with the aid of the weighted modulus of continuity

Bu çalışmada, çok gruplu sınıflandırma problemlerinin çözümü için regresyon analizi ve matematiksel programlamaya dayalı iki aşamalı yeni bir hibrit sınıflandırma yöntemi geliştirilmiştir. Önerilen yöntemin ilk aşamasında, her bir birimin sınıflandırma skoru her birim için oluşturulan doğrusal regresyon denklemi yardımıyla tahmin edilmektedir. İkinci aşamasında ise, birimlerin sınıflandırılması kümeleme analizi tabanlı matematiksel programlama modeli ile yapılmaktadır. Önerilen yöntem kendisini oluşturan regresyon analizi ve matematiksel programlama yöntemlerinin güçlü yanlarını kombine etmektedir. Literatürden alınan 10 gerçek veri seti ve simülasyon çalışması sonuçlarından, önerilen yöntemin regresyon analizi, matematiksel programlama ve yapay sinir ağı temelli sınıflandırma yöntemlerine göre daha iyi performans gösterdiği gözlemlenmiştir.

The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and A-statistical convergence are established. Our results are based on a ρ function. These results include the preservation properties of the classical Baskakov operators.

In this paper, we investigate a variant of the Jain operators, which preserve the linear functions. We compute the rate of convergence of these operators with the help of K-functional. We also introduce modifications of the Jain operators based on the models in [4] and [10]. These modified operators yield better error estimates than the Jain operators.

We introduce certain modified Sz\'{a}sz-Mirakyan operators in polynomial weighted spaces of functions of one variable. We studied approximation properties of these operators.

The present paper deals with approximation properties of q-Szász-Mirakyan-Kantorovich operators. We construct new bivariate generalization by -integral and these operators' approximation properties in polynomial weighted spaces are investigated. Also, we obtain Voronovskaya-type theorem for the proposed operators in polynomial weighted spaces of functions of two variables.