Browsing by Author "Akdemir, Ahmet Ocak"

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(h, m) - Convex functions on delta = [a, b] x [c, d] and hadamard-type integral inequality
(Amer Inst Physics, 2017) Akdemir, Ahmet Ocak; Ekinci, A.; Han, I.; Set, E.; Dadaşoglu, F.; Karagöz, K.; Öztekin, A.; Özdemir, Muhammet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Bölümü.; AAH-1091-2021; 22734889600
In this paper, we define (h, m) convex functions on Delta = [a, b] x [c, d] and obtain sonic properties of this new class of functions. We also prove a new generalization of Hadamard inequality on the co-ordinates.
Hadamard type inequalities for m -convex and (α, m)-convex functions via fractional integrals
(Amer Inst Physics, 2018) Ardıç, Merve Avcı; Ekinci, Alper; Akdemir, Ahmet Ocak; Tosun, M.; Ersoy, S.; İlarslan, K.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi.; AAH-1091-2021; 22734889600
In this paper, we established some new Hadamard-type integral inequalities for functions whose derivatives of absolute values are m-convex and (alpha, m) convex functions via Riemann-Liouville fractional integrals.
Integral inequalities for co-ordinated s-convex functions
(Amer Phyical Society, 2017) Akdemir, Ahmet Ocak; Ekinci, A; Han, I.; Set, E.; Dadaşoglu, F.; Karagöz, K.; Öztekin, A.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Bölümü.; AAH-1091-2021; 22734889600
In the present note, we obtain some new integral inequalities for co-ordinated s -convex functions by using an integral identity.
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
New integral inequalities for co-ordinated m-convex functions
(American Institute of Physics, 2016-04-18) Akdemir, Ahmet Ocak; Aslan, I.; Bayrak, Y.; Akdemir, A. O.; Ekinci, A.; Polat, K.; Dadaşoğlu, F.; Türkoğlu, E. A.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Bölümü.; AAH-1091-2021; 22734889600
In this paper, we prove some new integral inequalities for co-ordinated m -convex functions by using a new integral identity and basic definitions. We also give some reduced results by selecting special value of parameter m.
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-1091-2021
In 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.
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 Hadamard-type inequalities for co-ordinated r -convex functions
(Amer, 2017-04-25) Ekinci, Alper; Akdemir, Ahmet Ocak; Akdemir, A. O.; Ekinci, A.; Han, I.; Set, E.; Dadaşoglu, F.; Karagöz, K.; Öztekin, A.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Bölümü.; AAH-1091-2021; 22734889600
In this paper we defined r-convexity on the co-ordinates and we established some Hadamard-Type inequalities.
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.
Several inequalities for log-convex functions
(Elsevier Science Bv, 2018-08-01) Ardıç, Merve Avcı; Akdemir, Ahmet Ocak; Özdemir, M. Emin; Bursa Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Bölümü.; AAH-1091-2021
In this paper, we recall Ostrowski's inequality, Hadamard's inequality and the definition of log-convex functions. We also mention an useful integral identity in the first part of our study. The second part of our study includes new results. We prove new generalizations for log-convex functions. Several new Ostrowski type inequalities have been established and some special cases have been given by choosing h = 0 or x = a+b/2
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 Hermite-Hadamard type inequalities for (α, m)-convex functions on the co-ordinates
(American Institute of Physics, 2016) Akdemir, Ahmet Ocak; Aslan, I.; Bayrak, Y; Ekinci, A.; Polat, K.; Dadaşoğlu, F.; Türkoğlu, E. A.; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Öğretmenliği Bölümü.; AAH-1091-2021; 22734889600
In this study, we prove some Hermite-Hadamard type integral inequalities for (alpha, m) -convex functions on the co-ordinates on Delta.
Some new generalizations for GA–convex functions
(Univ Nis, 2016-04-12) Akdemir, Ahmet Ocak; Ardıç, Merve Avcı; Yalçın, Abdullatif; Özdemir, Muhamet Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Bölümü.; AAH-1091-2021; 22734889600
In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity : Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.
Some new integral inequalities for functions whose derivatives of absolute values are convex and concave
(Institute of Applied Mathematics, 2019) Ekinci, Alper; Akdemir, Ahmet Ocak; Özdemir, M. Emin; Uludağ Üniversitesi/Eğitim Fakültesi/Matematik Bölümü.; 0000-0002-5992-094X; AAH-1091-2021
In this paper, we prove some new inequalities for the functions whose derivatives' absolute values are convex and concave by dividing the interval [a, b] to n + 1 equal even sub-intervals. We obtain some new results involving intermediate values of vertical bar f'vertical bar in [a, b] by using some classical inequalities like Hermite-Hadamard, Holder and Power-Mean.