Browsing by Author "Set, Erhan"

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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-1091-2021
The 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.
Chebyshev type inequalities involving extended generalized fractional integral operators
(American Institute of Mathematical Sciences, 2020-03-27) Set, Erhan; Demirbaş, Sevdenur; Özdemir, M. Emin; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Bölümü.; 0000-0003-1364-5396; 22734889600
In this paper, mainly by using the extended generalized fractional integral operator that involve a further extension of Mittag-Leffler function in the kernel, we obtain several fractional Chebyshev type integral inequalities. So, results of Dahmani et al. from [4] are generalized. Also, it is point out that new results are obtained for different fractional integral operators with the help of special selection of parameters.
Grüss type inequalities involving new conformable fractional integral operators
(Amer Inst Physics, 2018) Set, Erhan; Mumcu, İlker; Sarıkaya, M. Z.; Akdemir, A. O.; Ekinci, A.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Bölümü.; AAH-1091-2021; 22734889600
A number of Gruss type inequalities involving various fractional integral operators have, recently, been presented. Here, motivated essentially by the earlier works and their applications in diverse research subjects, we aim to establish several Gruss type inequalities involving generalized new conformable fractional integral operator.
M geometrically convex functions and hadamard type inequalities via riemann-liouville integrals
(Baku State Univ, Inst Applied Mathematics, 2020-01-01) Akdemir, Ahmet Ocak; Set, Erhan; Fikret, A; Tamer, B; Özdemir, M. Emin; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/; Fikret, A; Tamer, B; AAH-1091-2021
Novel generalizations for gruss type inequalities pertaining to the constant proportional fractional integrals
(Ministry Communications & High Technologies Republic Azerbaijan, 2023-01-01) Çelik, Barış; Set, Erhan; Akdemir, Ahmet Ocak; Özdemir, M. Emin; ÖLMEZ, Emine Büşra (ÖZDEMİR); Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Eğitimi Bölümü; JIH-1630-2023
In this study, motivating and new findings are proved mainly by using the strong link between fractional analysis and inequality theory. Some new and general versions of the Gruss inequality, which has an important place in the literature, are presented with the help of the constant proportional (CP) fractional integral operator. In the methodology of obtaining the findings, the kernel structure of the fractional integral operator, the properties of the operator, the properties of the functions in the hypotheses and the well-known analysis processes were taken into account.
On integral inequalities related to the weighted and the extended Chebyshev functionals involving different fractional operators
(Springer, 2020-11-09) Çelik, Barış; Set, Erhan; Gürbüz, Mustafa Çağrı; Özdemir, Muhammet Emin; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Eğitimi Bölümü.; 0000-0003-1851-2672; 0000-0003-1364-5396; ABF-6613-2020; AAH-1091-2021; 57215932419; 22734889600
The role of fractional integral operators can be found as one of the best ways to generalize classical inequalities. In this paper, we use different fractional integral operators to produce some inequalities for the weighted and the extended Chebyshev functionals. The results are more general than the available classical results in the literature.
On new fractional Hermite-Hadamard type inequalities for n-time differentiable quasi-convex functions and P-functions
(Amer Inst Physics, 2017) Set, Erhan; Alan, E. Aykan; Akdemir, A. O.; Ekinci, A.; Han, I.; Set, E.; Dadaşoğlu, F.; Karagöz, K.; Öztekin, A.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/İlköğretim Bölümü.; AAH-1091-2021; 22734889600
In this article, by using the Hölder's inequality and power mean inequality the authors establish several inequalities of Hermite-Hadamard type for n- time differentiable quasi-convex functions and P- functions involving Riemann-Liouville fractional integrals.
On new Simpson type inequalities for quasi-convex functions via Riemann-Liouville integrals
(Amer Inst Physic, 2016) Set, Erhan; Uygun, Nazlı; Aslan, I.; Bayrak, Y.; Akdemir, A. O.; Ekinci, A.; Polat, K.; Dadaşoğlu, F.; Türkoğlu, E. A.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/İlköğretim Bölümü.; AAH-1091-2021; 22734889600
In this note, some new Simpson-type inequalities for functions whose derivatives of absolute value are quasi-convex functions with the help of Riemann-Liouville fractional integrals are obtained. Also by special selections of n and alpha we give some reduced results.
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-2400-2019
An 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.
Ostrowski-type inequalities for strongly convex functions
(Walter de Gruyter Gmbh, 2018) Set, Erhan; Sarıkaya, Mehmet Zeki; Akdemir, Ahmet Ocak; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Eğitimi Bölümü.; AAH-1091-2021; 22734889600
In this paper, we establish Ostrowski-type inequalities for strongly convex functions, by using some classical inequalities and elementary analysis. We also give some results for the product of two strongly convex functions.
Simpson type integral inequalities for convex functions via riemann-liouville integrals
(University Nis, 2017-03-29) Set, Erhan; Akdemir, Ahmet Ocak; Emin, Özdemir M.; Uludağ Üniversitesi/Eğitim Fakültesi/İlköğretim Bölümü.; AAH-1091-2021; 22734889600
In this paper some new inequalities of Simpson-type are established for the classes of functions whose derivatives of absolute values are convex functions via Riemann-Liouville integrals. Also, by special selections of n,we give some reduced results.
Some new results on hermite-hadamard-mercer-type inequalities using a general family of fractional integral operators
(MDPİ, 2021-09-01) Set, Erhan; Celik, Baris; Aslan, Mucahit; Özdemir, M. Emin; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Bölümü.; 0000-0001-5372-7543; ABF-6613-2020; AAH-1091-2021
The aim of this article is to obtain new Hermite-Hadamard-Mercer-type inequalities using Raina's fractional integral operators. We present some distinct and novel fractional Hermite-Hadamard-Mercer-type inequalities for the functions whose absolute value of derivatives are convex. Our main findings are generalizations and extensions of some results that existed in the literature.