(p,q)-Generalization of Szasz-Mirakyan Operators

In this paper, we introduce new modifications of Szasz-Mirakyan operators based on (p,q)-integers. We first give a recurrence relation for the moments of new operators and present explicit formula for the moments and central moments up to order 4. Some approximation properties of new operators are explored: the uniform convergence over bounded and unbounded intervals is established, direct approximation properties of the operators in terms of the moduli of smoothness is obtained and Voronovskaya theorem is presented. For the particular case p=1, the previous results for q-Szasz-Mirakyan operators are captured

A pair-wise scaling study on the missions of education supervisors in Turkey

The purpose of this study is to specify the mission that the education experts consider as preferential by providing a pair-wise comparison of their missions. The study group includes 174 education supervisors who are on duty in the primary school section of 56 different provinces. “Evaluation Form of Education Supervisors’ Mission Priorities” has been used as the data collection tool. Evaluation form of education supervisors’ mission priorities were scaled from complete data matrix with Thurstone’s law of comparative judgment case V. Equation. After the scaling operation, the inner consistency of supervisor judgments, the extent of agreement among supervisors and the significance of these were examined. For this process, two statistics called Kendall’s zeta statistics and Kendall’s U statistics were used. The results of this study have revealed that “counseling and in service training” is considered as a primary mission by education supervisors. Guidance and on site training is followed by “inspection and evaluation”, “research”, and lastly “inquisition”. In addition, the education supervisor can be considered as consistent in her/his judgment and the education supervisors’ judgments are considered in agreement.Key words: The education supervisor, supervision, scaling

Approximation properties of two dimensional Bernstein-Stancu-Chlodowsky operators

In this paper, as a generalization of Bernstein-Stancu type operators of two variable, we introduce a new positive linear operator called Bernstein-Stancu-Chlodowsky on a triangular domain, with mobile boundaries, which extends to [0, ∞) × [0, ∞) as n → ∞. We give some shape properties that are preserved and also obtain weighted approximation properties of these operators

Operator Methods in Approximation Theory

n/

On Sequences of J. P. King-Type Operators

This survey is devoted to a series of investigations developed in the last fifteen years, starting from the introduction of a sequence of positive linear operators which modify the classical Bernstein operators in order to reproduce constant functions and x2 on [0,1]. Nowadays, these operators are known as King operators, in honor of J. P. King who defined them, and they have been a source of inspiration for many scholars. In this paper we try to take stock of the situation and highlight the state of the art, hoping that this will be a useful tool for all people who intend to extend King's approach to some new contents within Approximation Theory. In particular, we recall the main results concerning certain King-type modifications of two well known sequences of positive linear operators, the Bernstein operators and the Szász-Mirakyan operators

Beyazlatma sonrasında antioksidan uygulamasının minenin bağlanma kuvvetine etkisi

Amaç: Bu çalışmanın amacı, % 10 sodyum askorbat (SA), %6.5 üzüm çekirdeği özü (ÜÇÖ) ve % 10 alfa-tokoferol (α-TP)’ ün farklı uygulama sürelerinde, beyazlatılmış mineye, adeziv rezin simanın makaslama bağlanma kuvvetini değerlendirmektir.Gereç ve Yöntemler: 108 adet insan üst santral dişi 9 gruba ayrılmıştır (n:12). Kontrol grubu dışındaki bütün gruplara % 40’lık hidrojen peroksit (HP) kullanarak beyazlatma işlemi uygulanmıştır. Gruplar; GK: Beyazlatma uygulanmadan restorasyon yapılan (kontrol grubu), GB: Beyazlatma yapıldıktan sonra restorasyon yapılan, GT7g: Yapay tükürükte 7 gün bekledikten sonra restorasyon yapılan, GSA15: 15 dakika süreyle % 10 SA uygulandıktan sonra restorasyon yapılan, GSA60: 60 dakika süreyle % 10 SA uygulandıktan sonra restorasyon yapılan, Gα-TP15: 15 dakika süreyle % 10 α-TP uygulandıktan sonra restorasyon yapılan, Gα-TP60: 60 dakika süreyle % 10 α-TP uygulandıktan sonra restorasyon yapılan, GÜÇÖ15: 15 dakika süreyle % 6.5 ÜÇÖ uygulandıktan sonra restorasyon yapılan, GÜÇÖ60: 60 dakika süreyle %6.5 ÜÇÖ uygulandıktan sonra restorasyon yapılan. Antioksidan uygulamasından hemen sonra, indirekt restorasyonlar adeziv rezin simanla diş yüzeyine bağlanmıştır. Örnekler distile suda 24 saat 37°C’de bekletildikten sonra, makaslama bağlanma kuvveti testi yapılmıştır. Kırılma tipleri stereomikroskop altında değerlendirilmiştir. Veriler tek yönlü varyans analizi, Levene ve Tukey HSD testleri kullanılarak yapılmıştır (

Asymptotic Formulas for Generalized Szasz-Mirakyan Operators

Acar, Tuncer/0000-0003-0982-9459WOS: 000355144500020In the present paper, we consider the general Szasz-Mirakyan operators and investigate their asymptotic behaviours. We obtain quantitative Voronovskaya and quantitative Gruss type Voronovskaya theorems using the weighted modulus of continuity. The particular cases are presented for classical Szasz-Mirakyan operators. (C) 2015 Elsevier Inc. All rights reserved