Browsing by Author "Ozger, Faruk"

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Approximation by a New Stancu Variant of Generalized (Λ, Μ)-Bernstein Operators
(Elsevier, 2024) Cai, Qing-Bo; Aslan, Resat; Ozger, Faruk; Srivastava, Hari Mohan
The primary objective of this work is to explore various approximation properties of Stancu variant generalized (lambda, mu)-Bernstein operators. Various moment estimates are analyzed, and several aspects of local direct approximation theorems are investigated. Additionally, further approximation features of newly defined operators are delved into, such as the Voronovskaya-type asymptotic theorem and pointwise estimates. By comparing the proposed operator graphically and numerically with some linear positive operators known in the literature, it is evident that much better approximation results are achieved in terms of convergence behavior, calculation efficiency, and consistency. Finally, the newly defined operators are used to obtain a numerical solution for a special case of the fractional Volterra integral equation of the second kind.
Some Approximation Results on a Class of Szász-Mirakjan Operators Including Non-Negative Parameter Α
(Taylor & Francis inc, 2025) Ozger, Faruk; Aslan, Resat; Ersoy, Merve
Alternative proofs of the Weierstrass uniform approximation theorem have been provided by numerous mathematicians, including renowned ones. Among them, there was Bernstein that used a set of polynomials known as the Bernstein polynomials. Motivated by the advancements in computational disciplines, we propose a new type of Sz & aacute;sz-Mirakjan-Kantorovich operators that incorporate a shape parameter alpha. Certain shape-preserving properties, such as monotonicity and convexity, are achieved by computing the first and second order derivatives of the proposed operators. Certain approximation properties, including the statistical rate of convergence, are also obtained using a regular summability matrix. Finally, theoretical results are supported by illustrative graphics and numerical experiments using the Mathematica computer program. The operators defined in this paper may be used in computer and computational sciences, including in robotic manipulator control.