Browsing by Author "Bayraktar, B."

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About an algorithm of function approximation by the linear splines
(Turkic World Mathematical Soc, 2016-01-01) Kudaev, V.; Bayraktar, B.; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi.; 0000-0001-7594-8291; ABI-7823-2020
The actual application for the problem of best approximation of grid functionby linear splines was formulated. A mathematical model and a method for its solution were developed. Complexity of the problem was that it was multi - extremal and could not be solved analytically. The method was developed in order to solve the problem of dynamic programming scheme, which was extended by us. Given the application of the method to the problem of flow control in the pressure-regulating systems, the pipeline network for transport of substances (pipelines of water, oil, gas, and etc.) that minimizes the amount of substance reservoirs and reduces the discharge of substance from the system. The method and the algorithm developed here may be used in computational mathematics, optimal control and regulation system, and regressive analysis.
Grid function approximation by linear splines with minimum deviation
(Scibulcom, 2015-01-01) Bayraktar, B.; Kudaev, V.; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik ve Fen Bilimleri Eğitimi Bölümü.; 0000-0001-7594-8291; ABI-7823-2020
The actual application for the problem of best approximation of grid function by linear splines was formulated. A mathematical model and method of its solution were developed. Complexity of the problem was that it was multi-extremal and can not be solved analytically. This fact assumed the need to develop an efficient algorithm for solving the problem.The method was developed for solving the problem of dynamic programming scheme, which was extended by us. In some studies, a similar problem was solved locally, and their solution did not include a large number of segments. However, in this paper, the problem was solved globally with defect delta.Given the application of the method to the problem of flow control in the pressure regulating systems, the pipeline network for transport of substances (pipelines of oil, gas, water, etc.) minimises the amount of substance in reservoirs and reduces the discharge of substance from the system. The method and algorithm developed may be used in computational mathematics, optimum control and regulation system, and regressive analysis.
Several new integral inequalities via k- riemann- liouville fractional integrals operators
(Petrozavodsk State, 2021-01-01) Butt, S., I; Umar, M.; Bayraktar, B.; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi.; 0000-0001-7594-8291; ABI-7823-2020
The main objective of this paper is to establish several new integral inequalities including k-Riemann - Liouville fractional integrals for convex, s-Godunova - Levin convex functions, quasi-convex, eta-quasi-convex. In order to obtain our results, we have used classical inequalities as Holder inequality, Power mean inequality and Weighted Holder inequality. We also give some applications.
Some new integral inequalities for (s, m)-convex and (α, m)-convex functions
(Karaganda State Univ, 2019-01-01) Bayraktar, B.; Kudaev, V. Ch.; BAYRAKTAR, BAHTİYAR; Uludağ Üniversitesi/Matematik ve Fen Bilimleri Eğitimi Bölümü; 0000-0001-7594-8291; ABI-7823-2020
The paper considers several new integral inequalities for functions the second derivatives of which, withrespect to the absolute value, are (s, m)-convex and (alpha, m)-convex functions. These results are relatedto well-known Hermite-Hadamard type integral inequality, Simpson type integral inequality, and Jensentype inequality. In other words, new upper bounds for these inequalities using the indicated classes ofconvex functions have been obtained. These estimates are obtained using a direct definition for a convexfunction, classical integral inequalities of Holder and power mean types. Along with the new outcomes, thepaper presents results confirming the existing in literature upper bound estimates for integral inequalities(in particular well known in literature results obtained by U. Kirmaci in [7] and M.Z. Sarikaya and N. Aktanin [35]). The last section presents some applications of the obtained estimates for special computing facilities(arithmetic, logarithmic, generalized logarithmic average and harmonic average for various quantities)