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Öğe GENERALIZATION OF CEBYSEV TYPE INEQUALITIES FOR FIRST DIFFERENTIABLE MAPPINGS(Univ Miskolc Inst Math, 2011) Set, Erhan; Sarıkaya, Mehmet Zeki; Ahmad, FarooqIn this paper, we improve and further generalize some Cebysev type inequalities involving functions whose derivatives belong to L-p spaces via certain integral identities.Öğe A GENERALIZATION OF Cˇ EBYSˇEV TYPE INEQUALITIES FOR FIRST DIFFERENTIABLE MAPPINGS(2011) Set, Erhan; Sarıkaya, Mehmet Zeki; Ahmad, FarooqIn this paper, we improve and further generalize some ?ebys?v type inequalities involving functions whose derivatives belong to L p spaces via certain integral identities. © 2011 Miskolc University Press.Öğe Generalizations of Different Type Inequalities for $s$-Convex, Quasi-Convex and $P$-Function(Mehmet Zeki SARIKAYA, 2022) Sarıkaya, Mehmet Zeki; Çelik, Barış; Set, Erhan; Azaklı, HanifeThe main purpose of this article is to present the Bullen, Midpoint, Trapezoid and Simpson type inequalities, respectively, for different classes of convexity, with the help of identities existing in the literature.Öğe GENERALIZED OSTROWSKI TYPE INEQUALITIES FOR FUNCTIONS WHOSE LOCAL FRACTIONAL DERIVATIVES ARE GENERALIZED s-CONVEX IN THE SECOND SENSE(Czestochowa Univ Technology, Inst Mathematics, 2016) Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Set, ErhanIn this paper, we establish some generalized Ostrowski type inequalities for functions whose local fractional derivatives are generalized s-convex in the second sense.Öğe Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense via fractional integrals(Tusi Mathematical Research Group (TMRG), 2015) Set, Erhan; Özdemir, Muhamet Emin; Sarıkaya, Mehmet Zeki; Karakoç, FilizIn this paper we establish Hermite-Hadamard type inequalities for mappings whose derivatives are s-convex in the second sense and concave. © 2015, Khayyam Journal of Mathematics.Öğe Hermite-Hadamard Type Riemann-Liouville Fractional Integral Inequalities for Convex Functions(Amer Inst Physics, 2016) Tomar, Muharrem; Set, Erhan; Sarıkaya, Mehmet ZekiIn this paper, we prove a useful lemma. After that, using this lemma, we obtain several new Hermite-Hadamard type of inequalities for Reimann-Liouville fractional integrals.Öğe Hermite-Hadamard's inequalities for fractional integrals and related fractional inequalities(Pergamon-Elsevier Science Ltd, 2013) Sarıkaya, Mehmet Zeki; Set, Erhan; Yaldız, Hatice; Başak, NagihanIn the present note, first we have established Hermite-Hadamard's inequalities for fractional integrals. Second, an integral identity and some Hermite-Hadamard type integral inequalities for the fractional integrals are obtained and these results have some relationships with [S.S. Dragomir, R.P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (5) (1998), 91-95)]. (C) 2011 Elsevier Ltd. All rights reserved.Öğe INEQUALITIES OF HERMITE-HADAMARD TYPE FOR FUNCTIONS WHOSE DERIVATIVES ABSOLUTE VALUES ARE m-CONVEX(Amer Inst Physics, 2010) Set, Erhan; Özdemir, Mehmet Emin; Sarıkaya, Mehmet ZekiIn this paper, we establish several inequalities of Hermite-Hadamard type for functions whose derivatives absolute values are m-convex.Öğe A New General Inequality for Double Integrals(Amer Inst Physics, 2012) Set, Erhan; Sarıkaya, Mehmet Zeki; Akdemir, Ahmet OcakIn this paper, we obtain a new general inequality involving functions of two independent variables.Öğe New Inequalities of Hadamard Type for Quasi-Convex Functions(Amer Inst Physics, 2012) Özdemir, Mehmet Emin; Yıldız, Çetin; Akdemir, Ahmet Ocak; Set, ErhanIn this paper some new Hadamard-type inequalities for functions whose second derivatives in absolute values are quasi-convex are established. Our results gives new estimations for quasi-convex functions.Öğe New inequalities of Ostrowski type for mappings whose derivatives are s-convex in the second sense via fractional integrals(Pergamon-Elsevier Science Ltd, 2012) Set, ErhanA new identity similar to an identity proved in Alomari et al. (2010) [15] for fractional integrals is established. Then by making use of the established identity, some new Ostrowski type inequalities for Riemann-Liouville fractional integral are established. Our results have some relationships with the results of Alomari et al. (2010), proved in [15] and the analysis used in the proofs is simple. (C) 2011 Elsevier Ltd. All rights reserved.Öğe New some Hadamard's type inequalities for co-ordinated convex functions(2012) Sarıkaya, Mehmet Zeki; Set, Erhan; Özdemir, Mehmet Emin; Dragomir, Silvestru SeverIn this paper, we establish new some Hermite-Hadamard's type in-equalities of convex functions of 2-variables on the co-ordinates.Öğe On a new ostrowski-type inequality and related results(Kyungpook National University, 2014) Set, Erhan; Sarıkaya, Mehmet ZekiWe provide a new Ostrowski-type inequality involving functions of two independent variables, as well as some related results.Öğe On Generalization of Trapezoid Type Inequalities for s-Convex Functions with Generalized Fractional Integral Operators(Univ Nis, Fac Sci Math, 2018) Usta, Fuat; Budak, Hüseyin; Sarıkaya, Mehmet Zeki; Set, ErhanBy using contemporary theory of inequalities, this study is devoted to propose a number of refinements inequalities for the Hermite Hadamard's type inequality and conclude explicit bounds for the trapezoid inequalities in terms of s-convex mappings, at most second derivative through the instrument of generalized fractional integral operator and a considerable amount of results for special means. The results of this study which are the generalization of those given in earlier works are obtained for functions f where vertical bar f'vertical bar and vertical bar f ''vertical bar (or vertical bar f'vertical bar(q) and vertical bar f ''vertical bar(q) for q >= 1) are s-convex hold by applying the Holder inequality and the power mean inequality.Öğe On generalizations of the hadamard inequality for (?, m)-Convex functions(2012) Set, Erhan; Sardari, Maryam; Özdemir, Muhamet Emin; Rooin, JamalIn this paper we establish several Hadamard-type integral inequalities for (?, m) -convex functions.Öğe On generalized Gruss type inequalities for k-fractional integrals(Elsevier Science Inc, 2015) Set, Erhan; Tomar, Muharrem; Sarıkaya, Mehmet ZekiThe aim of the present paper is to investigate some new integral inequalities of Gruss type for k - Riemann-Liouville fractional integrals. From our results, new weighted or classical Griiss type inequalities have been established for some special cases. Moreover, special cases of the integral inequalities in this paper have been obtained by Dahmani and Tabharit, 2010 in [5]. (C) 2015 Elsevier Inc. All rights reserved.Öğe On new inequalities of Hermite-Hadamard-Fejer type for convex functions via fractional integrals(Elsevier Science Inc, 2015) Set, Erhan; İşcan, İmdat; Sarıkaya, Mehmet Zeki; Özdemir, Mehmet EminIn this paper, we establish some weighted fractional inequalities for differentiable mappings whose derivatives in absolute value are convex. These results are connected with the celebrated Hermite-Hadamard-Fejer type integral inequality. The results presented here would provide extensions of those given in earlier works. (C) 2015 Elsevier Inc. All rights reserved.Öğe On new inequalities of Simpson's type for Quasi-Convex functions with applications(2012) Set, Erhan; Özdemir, Muhamet Emin; Sarıkaya, Mehmet ZekiIn this paper, we introduce some inequalities of Simpson's type based on quasiconvexity. Some applications for special means of real numbers are also given.Öğe On new inequalities of Simpson's type for s-convex functions(Pergamon-Elsevier Science Ltd, 2010) Sarıkaya, Mehmet Zeki; Set, Erhan; Özdemir, Mehmet EminIn this paper, we establish some new inequalities of Simpson's type based on s-convexity. Some applications to special means of real numbers are also given. (C) 2010 Elsevier Ltd. All rights reserved.Öğe On new Ostrowski type integral inequalities(Chiang Mai University, 2014) Sarıkaya, Mehmet Zeki; Set, ErhanIn this article, we give a new Montgomery type identity and using this identity establish a new Ostrowski type inequality and its perturbed inequality forms. © 2014 by the Mathematical Association of Thailand. All rights reserved.
