Yazar "Ansari, Khursheed J." seçeneğine göre listele
Listeleniyor 1 - 5 / 5
Sayfa Başına Sonuç
Sıralama seçenekleri
Öğe Approximation properties of a new family of Gamma operators and their applications(Springer, 2021) Özçelik, Reyhan; Kara, Emrah Evren; Usta, Fuat; Ansari, Khursheed J.The present paper introduces a new modification of Gamma operators that protects polynomials in the sense of the Bohman-Korovkin theorem. In order to examine their approximation behaviours, the approximation properties of the newly introduced operators such as Voronovskaya-type theorems, rate of convergence, weighted approximation, and pointwise estimates are presented. Finally, we present some numerical examples to verify that the newly constructed operators are an approximation procedure.Öğe A Generalization of Szasz-Mirakyan Operators Based on alpha Non-Negative Parameter(Mdpi, 2022) Ansari, Khursheed J.; Usta, FuatThe main purpose of this paper is to define a new family of Szasz-Mirakyan operators that depends on a non-negative parameter, say alpha. This new family of Szasz-Mirakyan operators is crucial in that it includes both the existing Szasz-Mirakyan operator and allows the construction of new operators for different values of alpha. Then, the convergence properties of the new operators with the aid of the Popoviciu-Bohman-Korovkin theorem-type property are presented. The Voronovskaja-type theorem and rate of convergence are provided in a detailed proof. Furthermore, with the help of the classical modulus of continuity, we deduce an upper bound for the error of the new operator. In addition to these, in order to show that the convex or monotonic functions produced convex or monotonic operators, we obtain shape-preserving properties of the new family of Szasz-Mirakyan operators. The symmetry of the properties of the classical Szasz-Mirakyan operator and of the properties of the new sequence is investigated. Moreover, we compare this operator with its classical correspondence to show that the new one has superior properties. Finally, some numerical illustrative examples are presented to strengthen our theoretical results.Öğe Jain's operator: A new construction and applications in approximation theory(Wiley, 2023) Ansari, Khursheed J.; Civelek, Muhammet; Usta, FuatThe new and more comprehensive Jain-type operators based on a function tau and two sequences of functions pn and qn have been introduced. This newly defined operator has an important place in which these three functions can create both existing and new operators with special selections. In order to show their approximation properties, we present direct approximation results and Voronovkskaya-type results for these operators. Finally, we provide a series of numerical examples to show their performance visually.Öğe A Note on New Construction of Meyer-Konig and Zeller Operators and Its Approximation Properties(Mdpi, 2021) Cai, Qing-Bo; Ansari, Khursheed J.; Usta, FuatThe topic of approximation with positive linear operators in contemporary functional analysis and theory of functions has emerged in the last century. One of these operators is Meyer-Konig and Zeller operators and in this study a generalization of Meyer-Konig and Zeller type operators based on a function tau by using two sequences of functions will be presented. The most significant point is that the newly introduced operator preserves {1,tau,tau 2} instead of classical Korovkin test functions. Then asymptotic type formula, quantitative results, and local approximation properties of the introduced operators are given. Finally a numerical example performed by MATLAB is given to visualize the provided theoretical results.Öğe On approximation of Bernstein-Chlodowsky-Gadjiev type operators that fix e(-2x)(Springer, 2022) Okumuş, Feyza Tanberk; Akyiğit, Mahmut; Ansari, Khursheed J.; Usta, Fuatthat fix the function e(-2x) for x >= 0. Then, we provide the approximation properties of these newly defined operators for different types of function spaces. In addition, we focus on the rate of convergence utilizing appropriate moduli of continuity. Then, we provide the Voronovskaya-type theorem for these new operators. Finally, in order to validate our theoretical results, we provide some numerical experiments that are produced by a MATLAB complier.
