Person: BAYRAKTAR, BAHTİYAR
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BAYRAKTAR
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BAHTİYAR
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Publication Some generalized hadamard-type inequalities via fractional integrals(Pleiades Publishing Inc, 2021-02-01) Bayraktar, Bahtiyar; Attaev, Anatoly. Kh; Kudaev, V. Ch; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik ve Fen Bilimleri; 0000-0001-7594-8291; ABI-7823-2020In this paper, we establish some generalized inequalities of the Hermite-Hadamard type using fractional Riemann-Liouville integrals for the class of s-convex functions in the first and second sense. We assume that second derivatives of these functions are convex and take on values at intermediate points of the interval under consideration. We prove that this approach reduces the absolute error of Hadamard-type inequalities by a multiple of the number of intermediate points. In a particular case, the obtained upper bounds for the Hadamard inequality coincide with those given in the literature.Publication On some integral inequalities for (s,m) -convex functions(Türk Dünyası Matematik Topluluğu, 2020-01-01) Bayraktar, Bahtiyar; Gürbüz, Mustafa; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi; 0000-0001-7594-8291; ABI-7823-2020A new identity has been handled in this paper. It allows to derive new inequalities referring to upper estimation of the Jensen functional in the class of (s, m)-convex functions. Also some applications for special means are given by using new inequalities.Publication New integral inequalities of hermite-hadamard type in a generalized context(Univ Punjab, Dept Mathematics, 2021-01-01) Napoles Valdes, Juan Eduardo; Bayraktar, Bahtiyar; Butt, Saad İhsan; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Bilimleri Bölümü; 0000-0001-7594-8291; ABI-7823-2020In this paper, we obtained new integral inequalities of the Hermite-Hadamard type for convex and quasi-convex functions in a gen-eralized context.Publication Generalization of hadamard-type trapezoid inequalities for fractional integral operators(Inst Mathematics Computer Center Russia, 2021-03-01) Bayraktar, Bahtiyar; Özdemir, Muhamet Emin; BAYRAKTAR, BAHTİYAR; ÖZDEMİR, MUHAMET EMİN; 0000-0001-7594-8291; ABI-7823-2020; AAH-1091-2021The role of convexity theory in applied problems, especially in optimization problems, is well known. The integral Hermite-Hadamard inequality has a special place in this theory since it provides an upper bound for the mean value of a function. In solving applied problems from different fields of science and technology, along with the classical integro-differential calculus, fractional calculus plays an important role. A lot of research is devoted to obtaining an upper bound in the Hermite-Hadamard inequality using operators of fractional calculus.The article formulates and proves the identity with the participation of the fractional integration operator. Based on this identity, new generalized Hadamard-type integral inequalities are obtained for functions for which the second derivatives are convex and take values at intermediate points of the integration interval. These results are obtained using the convexity property of a function and two classical integral inequalities, the Hermite-Hadamard integral inequality and its other form, the power mean inequality. It is shown that the upper limit of the absolute error of inequality decreases in approximately n(2) times, where.. is the number of intermediate points. In a particular case, the obtained estimates are consistent with known estimates in the literature. The results obtained in the article can be used in further researches in the integro-differential fractional calculus.Publication Some new integral inequalities for (s,m)-convex and (α,m)-convex functions(Karaganda State Univ, 2019-01-01) Bayraktar, Bahtiyar; Kudaev, V. Ch.; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Matematik ve Fen Bilimleri Eğitimi Bölümü; 0000-0001-7594-8291; ABI-7823-2020The 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)Publication Some integral inequalities of hermite-hadamard type for differentiable (s,m)-convex functions via fractional integrals(Türk Dünyası Matematik Topluluğu, 2020-01-01) Bayraktar, Bahtiyar; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik ve Fen Bilimleri Eğitimi; 0000-0001-7594-8291; ABI-7823-2020In this paper, we present new inequalities connected with fractional integrals for twice differentiable functions derivatives which are (s, m) convex functions. To obtain this, integral inequalities were used classical inequalities as Holder inequalitiy and power mean inequality.This results are related to the well-known integral inequality of the Hermite-Hadamard type. Also some applications to special means are provided.Publication 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-7823-2020The 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.Publication 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-7823-2020The 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.Publication New extensions of hermite-hadamard inequality using k-fractional caputo derivatives(Tbilisi Centre Math Sci, 2023-06-01) Napoles, Juan E.; Bayraktar, Bahtiyar; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi; 0000-0003-2470-1090; 0000-0001-7594-8291; ABI-7823-2020By means of Caputo k-fractional derivatives, in this work, we obtain new extensions of the Hermite-Hadamard inequality for modified (h, m)- convex functions of the second type. At work, we show that some known results from the literature can be obtained as particular cases of the results presented here.Publication On generalizations of integral inequalities(Petrozavodsk State Univ, 2022-01-01) Napoles, J.; Rabossi, F.; Bayraktar, Bahtiyar; BAYRAKTAR, BAHTİYAR; Bursa Uludağ Üniversitesi/Eğitim Fakültesi.; 0000-0001-7594-8291; ABI-7823-2020In the present study, several new generalized integral inequalities of the Hadamard and Simpson-type are obtained. The results were obtained for functions whose first and third derivatives are either convex or satisfy the Lipschitz condition or the conditions of the Lagrange theorem. In a particular case, these results not only confirm but also improve some upper bounds, well known in the literature for the Simpson and Hermite-Hadamard-type inequali-ties.