Person: ÖZDEMİR, MUHAMET EMİN
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ÖZDEMİR
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MUHAMET EMİN
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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 Certain new hermite-hadamard type inequalities for convex functions via fractional integrals(Ankara Univ, Fac Sci, 2019-01-01) Set, Erhan; Korkut, Necla; Özdemir, M. Emin; ÖZDEMİR, MUHAMET EMİN; Bursa Uludağ Üniversitesi/Eğitim Fakültesi; AAH-1091-2021The object of this paper is to obtain certain Hermite-Hadamard type integral inequalities involving general class of fractional integral operators and the fractional integral operators with exponential kernel by using harmonically convex functions.Publication Generalized inequalities of hermite-hadamard type for convex functions(Etamaths, 2017-01-01) Yıldız, Çetin; Özdemir, Muhamet Emin; ÖZDEMİR, MUHAMET EMİN; Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü; AAH-1091-2021In this paper, new integral inequalities of Hermite-Hadamard type are developed for n-times differentiable convex functions. Also a parallel development is made base on concavity.Publication On the integral inequalities for riemann-liouville and conformable fractional integrals(Birkhauser, 2018-01-01) Akdemir, Ahmet Ocak; Set, Erhan; Ekinci, Alper; Agarwal, P; Dragomir, SS; Jleli, M; Samet, B; Özdemir, M. Emin; ÖZDEMİR, MUHAMET EMİN; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Anabilim Dalı.; Agarwal, P; Dragomir, SS; Jleli, M; Samet, B; 0000-0003-2466-0508; AAH-1091-2021; HKF-3376-2023; HKF-3391-2023; Q-2400-2019An integral operator is sometimes called an integral transformation. In the fractional analysis, Riemann-Liouville integral operator (transformation) of fractional integral is defined asS-alpha(x) = 1/Gamma(x) integral(x)(0) (x - t)(alpha-1) f(t)dtwhere f(t) is any integrable function on [0, 1] and alpha > 0, t is in domain of f.Publication New refinements and integral inequalities for concave functions(Turkic World Mathematical Soc, 2019-01-01) Akdemir, Ahmet Ocak; Özdemir, Muhammed Emin; ÖZDEMİR, MUHAMET EMİN; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Eğitimi Bölümü.; AAH-1091-2021In this paper, we establish new re finements and integral inequalities including concave functions. The reason why we choose the concave functions in this study is that the methods we use are applicable to these functions. Also some applications are provided.Publication New generalizations of ostrowski-like type inequalities for fractional integrals(Kyungpook Natl Univ, Dept Mathematics, 2016-03-01) Yıldız, Çetin; Sarıkaya, Mehmet Zeki; Özdemir, Muhamet Emin; ÖZDEMİR, MUHAMET EMİN; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Eğitimi Anabilim Dalı.; AAH-1091-2021In this paper, we use the Riemann-Liouville fractional integrals to establish several new inequalities for some differantiable mappings that are connected with the celebrated Ostrowski type integral inequality.