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Öğe Hermite-Hadamard Type Inequalities for (?, ?; n, m)-Logarithmically and (?, ?; n, m)-Godunova-Levin-Logarithmically Convex Functions(Amer Inst Physics, 2016) Acikel, Abdullah; Tunc, MevlutIn this paper, the Authors establish some new Hermite-Hadamard type inequalities for (beta, alpha; n, m) -logarithmic and (beta, alpha; n, m)-Godunova-Levin-log-convex functions. Some special cases are also discussed.Öğe On Opial Type Inequalities(Amer Inst Physics, 2016) Tunc, Mevlut; Gov, EsraIn this paper we establish some new integral inequalities analogous to the Opial inequality by using the proved lemma and some classical inequalities for convex functions.Öğe On some inequalities for functions whose absolute values of the second derivatives are ?-, m-, (?, m)-logarithmically convex(Walter De Gruyter Gmbh, 2015) Karabayir, Ibrahim; Tunc, Mevlut; Yuksel, EbruIn this paper, we establish some new Hadamard-type inequalities using elementary well-known inequalities for functions whose absolute values of the second derivatives are alpha-, m-, (alpha, m)-logarithmically convex.Öğe ON tgs-CONVEX FUNCTION AND THEIR INEQUALITIES(Univ Nis, 2015) Tunc, Mevlut; Gov, Esra; Sanal, UmmugulsumIn this paper, the authors define a new concept of the so-called tgs-convex function and establish some inequalities of the Hadamard type via ordinary and Riemann Liouville integral.Öğe Ostrowski type Inequalities for m- and (?, m)-geometrically convex functions via Riemann-Louville Fractional integrals(Springer Heidelberg, 2016) Tunc, MevlutIn this paper, some new inequalities of Ostrowski type established for the class of m- and (alpha, m)-geometrically convex functions which are generalizations of geometric convex functions.Öğe Ostrowski type inequalities for s-logarithmically convex functions in the second sense with applications(Walter De Gruyter Gmbh, 2015) Akdemir, Ahmet Ocak; Tunc, MevlutIn this paper, we establish some new Ostrowski type inequalities for s-logarithmically convex functions. Some applications of our results to PDFs and in numerical integration are given.Öğe Some Integral Inequalities via (p, q)-Calculus On Finite Intervals(Univ Nis, Fac Sci Math, 2021) Tunc, Mevlut; Gov, EsraThe aim of this paper is to construct (p, q)-calculus on finite intervals. The (p(k), q(k))-derivative and (p(k), q(k))-integral are defined and some basic properties are given. Also, (p(k), q(k))-analogue of Holder, Minkowski integral inequalities are proved.Öğe SOME NEW INEQUALITIES FOR DIFFERENTIABLE h-CONVEX FUNCTIONS AND APPLICATIONS(Univ Miskolc Inst Math, 2021) Cakmak, Musa; Tunc, Mevlut; Acem, AysegulIn this paper, the authors established a new identity for differentiable functions, afterwards they obtained some new inequalities for functions whose first derivatives in absolute value at certain powers are h-convex by using the identity. Also they give some applications for special means for arbitrary positive numbers.Öğe Some perturbed trapezoid inequalities for convex, s-convex and tgs-convex functions and applications(Tbilisi Centre Math Sci, 2015) Tunc, Mevlut; Sanal, UmmugulsumIn this paper,the Authors establish a new identity for twice differentiable functions. Afterwards some new inequalities are presented related to perturbed trapezoid inequality for the classes of functions wchose second derivatives of absolute values are convex, s-convex and tgs-convex. Last of all, applications to special menus have also been presented.Öğe SOME SIMPSON TYPE INTEGRAL INEQUALITIES FOR s-GEOMETRICALLY CONVEX FUNCTIONS WITH APPLICATIONS(Univ Studi Catania, Dipt Matematica, 2014) Kavurmaci-Onalan, Havva; Tunc, MevlutIn this paper, we establish some new Simpson type integral inequalities by using s- geometrically convex function which is given below as f(x(lambda) y(1-lambda) )<=[f (x)](lambda s) [f (y)] ((1-lambda)s) where f : I subset of R+-> R+ for some fixed s is an element of(0;1]; x; y is an element of I and lambda is an element of[0,1]. Also we get some applications for special means for positive numbers.
