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Öğe Bibliometric analysis of publications on house dust mites during 1980-2018(ELSEVIER ESPANA SLU, 2020) Demir, E.; Akmese, O. F.; Erbay, H.; Taylan-Ozkan, A.; Mumcuoglu, K. Y.Background: The global prevalence of allergic diseases has increased dramatically in recent years and are now recognized as significant chronic diseases worldwide. One of the most important allergens that causes allergic diseases is house dust mites. Objective: This study aims to present a bibliometric overview of research published on dust mites between 1980 and 2018. Methods: Articles published from 1980 to 2018 were analyzed using bibliometric methods. The keywords ?Dust mite*,? and ? Dermatophagoides ? were used in the Web of Science (WoS). Simple linear regression analysis was used to estimate the number of future publications on this subject. Results: A total of 4742 publications were found, 2552 (53.8%) of them were articles. Most of the articles were on subjects related to immunology (1274; 49.9%) and allergy (1229; 48.1%). Clinical and Experimental Allergy (222; 8.7%) was the journal with the most publications. The USA was the country that most contributed to the literature with 461 (18.1%) articles. The countries producing the most publications on this subject were developed countries. The most active author was W.R. Thomas (66; 2.5%). The most productive institution was the University of Western Australia (91; 3.6%). The most cited article was published in the New England Journal of Medicine .Conclusion: According to the findings, developed countries were the most productive in publishing on house dust mites. By planning multinational research rather than regional studies, it may be suggested that researchers in underdeveloped or developing countries could also-conduct more research on this subject.(C) 2019 SEICAP. Published by Elsevier Espana, S.L.U. All rights reserved.Öğe A Note on the Difference of Positive Operators and Numerical Aspects(SPRINGER BASEL AG, 2020) Aral, A.; Erbay, H.Recently, the differences between the two operators get the attention of scientists in approximation theory due to their ability to provide the approximation properties of the operator in the difference if the approximation properties of other operator in the difference are known. In other words, it gives us the ability to obtain a simultaneous approximation. On the other hand, the exponential-type operators possess better approximation properties than classical ones. Herein, the differences of the exponential-type Bernstein and Bernstein-Kantorovich operators and their differences between their higher order mu-derivatives applied to a function with the operators applied to the same order of mu-derivative of the function are considered. The estimates in the quantitative form are given in terms of the first modulus of continuity. Furthermore, quantitative estimates of the differences between Bernstein and Bernstein-Kantorovich operators as well as their Gruss-type difference are obtained. The numerical results obtained are in the direction of the theory, and some of them are presented.Öğe On Modified Mellin-Gauss-Weierstrass Convolution Operators(Springer Basel Ag, 2022) Aral, A.; Erbay, H.; Yilmaz, B.Mellin transform has various applications to real-life problems in function approximation, signal processing, and image recognition, thus, it has been the main ingredient of many studies in diverse fields. This study is devoted to Mellin operators and their variants to improve approximation accuracy and approximate ratio. Two Mellin type operators are reconstructed by using two sequences of functions to enable lower pointwise approximation error as well as higher pointwise convergence rate. Keeping the idea of Mellin convolution, these classes aim to be associated with functions defined on the semi-real axis, and the affine and quadratic functions pairs are fixed points. It has been shown, both theoretically and numerically, that operators can be used to approximate functions pointwise. Indeed the approximation accuracy can be adjusted by tuning the parameters. Moreover, weighted approximation, as well as Voronovskaya type results, are studied throughout the paper. The advantages of each operator over the other in terms of both approximation errors and convergence rates are presented.Öğe On Modified Mellin–Gauss–Weierstrass Convolution Operators(Birkhauser, 2022) Aral, A.; Erbay, H.; Yılmaz, B.Mellin transform has various applications to real-life problems in function approximation, signal processing, and image recognition, thus, it has been the main ingredient of many studies in diverse fields. This study is devoted to Mellin operators and their variants to improve approximation accuracy and approximate ratio. Two Mellin type operators are reconstructed by using two sequences of functions to enable lower pointwise approximation error as well as higher pointwise convergence rate. Keeping the idea of Mellin convolution, these classes aim to be associated with functions defined on the semi-real axis, and the affine and quadratic functions pairs are fixed points. It has been shown, both theoretically and numerically, that operators can be used to approximate functions pointwise. Indeed the approximation accuracy can be adjusted by tuning the parameters. Moreover, weighted approximation, as well as Voronovskaya type results, are studied throughout the paper. The advantages of each operator over the other in terms of both approximation errors and convergence rates are presented. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.Öğe The Picard and Gauss-Weierstrass Singular Integrals in (p, q)-Calculus(MALAYSIAN MATHEMATICAL SCIENCES SOC, 2020) Aral, A.; Deniz, E.; Erbay, H.The vast development of the techniques in both the quantum calculus and the post-quantum calculus leads to a significant increase in activities in approximation theory due to applications in computational science and engineering. Herein, we introduce (p, q)-Picard and (p, q)-Gauss-Weierstrass integral operators in terms of the (p, q)-Gamma integral. We give a general formula for the monomials under both (p, q)-Picard and (p, q)-Gauss-Weierstrass operators as well as some special cases. We discuss the uniform convergence properties of them. We show that both operators have optimal global smoothness preservation property via usual modulus of continuity. Finally, we establish the rate of approximation using the weighted modulus of smoothness. Depending on the choices of parameters p and q in the integrals, we are able to obtain better error estimation than classical ones.
