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Öğe GENERALIZED STEFFENSEN INEQUALITIES FOR LOCAL FRACTIONAL INTEGRALS(Etamaths Publ, 2017) Sarıkaya, Mehmet Zeki; Tunç, Tuba; Erden, SametFirstly we give a important integral inequality which is generalized Steffensen's inequality. Then, we establish weighted version of generalized Steffensen's inequality for local fractional integrals. Finally, we obtain several inequalities related these inequalities using the local fractional integral.Öğe Hermite-Hadamard type inequalities for interval-valued fractional integrals with respect to another function(Walter De Gruyter Gmbh, 2022) Tunç, TubaIn this paper, first we define interval-valued left-sided and right-sided fractional integrals of a function with respect to the another function. Then, we handle Hermite-Hadamard type inequalities via these definitions.Öğe Lokal kesirli integraller için yeni integral eşitsizlikleri ve uygulamaları(Düzce Üniversitesi, 2018) Tunç, Tuba; Sarıkaya, Mehmet ZekiMatematikte bilindiği üzere fraktal eğriler her yerde sürekli ama hiçbir yerde türevlenemezdir. Bundan dolayı klasik analiz bu gibi eğrilerin ele alınması ve karakterize edilmesi açısından yetersiz kalmıştır. Fraktal üzerindeki olayları tanımlamak ve sürekli ama hiçbir yerde türevlenemeyen fonksiyonların davranışlarını açıklamak için lokal kesirli analiz bir araç olmuştur. Buradan hareketle, lokal kesirli analiz teorisi ile ilgili literatürde var olmayan eşitsizliklerin elde edilmesi yoluyla lokal kesirli analiz alanına katkı sağlamak ve alandaki eksiklikleri gidermek tezin amacını oluşturmuştur. Bu amaç doğrultusunda, tez dört bölümden oluşmaktadır. İlk bölümde, eşitsizlik ve lokal kesirli analiz teorilerinin tarihsel sürecinden bahsedilmiştir. İkinci bölümde, üzerinde çalışılan Cantor fraktal kümesi hakkında bilgi verilmiştir. Ayrıca Yang tarafından kurulan ve yeni bir analiz oluşmasını sağlayan R^alpha uzayı ile ilgili bilgiler ve bu bilgilerden faydalanarak tanımlanan lokal kesirli limit, süreklilik, türev, integral için temel teoremler ve özellikler verilmiştir. Üçüncü bölümde, lokal kesirli integralden yararlanarak Steffensen, Cebyšev, Grüss gibi yeni eşitsizlikler elde edilmiştir. Son bölümde ise bu konu ile ilgili sonuç ve önerilere yer verilmiştir.Öğe New bounds for the Ostrowski-type inequalities via conformable fractional calculus(Springer Heidelberg, 2018) Usta, Fuat; Budak, Hüseyin; Tunç, Tuba; Sarıkaya, Mehmet ZekiIn this paper, we have introduced the new upper bounds for Ostrowski-type integral inequalities by using conformable fractional integral. In accordance with this purpose, we have benefited from the Taylor expansion for conformable fractional derivatives which was introduced by Anderson.Öğe New bounds for the Ostrowski-type inequalities via conformable fractional calculus (vol 7, pg 317, 2018)(Springer Heidelberg, 2018) Usta, Fuat; Budak, Hüseyin; Tunç, Tuba; Sarıkaya, Mehmet Zeki…Öğe New Midpoint-type Inequalities of Hermite-Hadamard Inequality with Tempered Fractional Integrals(2023) Tunç, Tuba; Altunok, Ayşe NurIn this research, we get some midpoint type inequalities of Hermite-Hadamard inequality via tempered fractional integrals. For this, we first obtain an identity. After that, using this identity and with the help of modulus function, Hölder inequality, power mean inequality, ongoing research and the papers mentioned, we have reached our intended midpoint type inequalities. Also, we give the special cases of our results. We see that our special results give earlier works.Öğe ON FUNCTIONAL GENERALIZATION OF OSTROWSKI INEQUALITY FOR CONFORMABLE FRACTIONAL INTEGRALS(Turkic World Mathematical Soc, 2018) Tunç, Tuba; Budak, Hüseyin; Sarıkaya, Mehmet ZekiIn this study, we establish a generalized Ostrowski type integral inequality for conformable fractional integrals. We also give some applications for p-norms and exponential.Öğe On generalized some integral inequalities for local fractional integrals(Elsevier Science Inc, 2016) Sarıkaya, Mehmet Zeki; Tunç, Tuba; Budak, HüseyinIn this study, we establish generalized Griiss type inequality and some generalized Cebysev type inequalities for local fractional integrals on fractal sets R-alpha (0 < alpha <= 1) of real line numbers. (C) 2015 Elsevier Inc.Öğe On Gruss Type Inequalities Utilizing Generalized Fractional Integral Operators(Amer Inst Physics, 2017) Tunç, Tuba; Usta, Fuat; Budak, Hüseyin; Sarıkaya, Mehmet ZekiIn this paper, some upper bounds of Gruss type inequalities are proven in the general sense for generalised fractional integral operators thus we unify corresponding integer and fractional order versions.Öğe On Hermite Hadamard-Type Inequalities Depending on The Metric Functions(Amer Inst Physics, 2016) Sarıkaya, Mehmet Zeki; Tunç, Tuba; Yaldız, HaticeIn this paper, a version of Hermite Hadamard-type inequalities for (d, t)-convex functions are established. And then we give some new inequalities of the Hermite-Hadamard type for the product of two (d, t)-convex functions.Öğe On Hermite-Hadamard Type Inequalities Via Fractional Integral Operators(Univ Nis, Fac Sci Math, 2019) Tunç, Tuba; Sarıkaya, Mehmet ZekiIn this paper, we give new definitions related to fractional integral operators for two variables functions using the class of integral operators. We are interested to give the Hermite-Hadamard inequality for a rectangle in plane via convex functions on co-ordinates involving fractional integral operators.Öğe On Integral Inequalities of Hermite-Hadamard Type Via Green Function and Applications(Prairie View A & M Univ, Dept Mathematics, 2019) Tunç, Tuba; Sönmezoğlu, Sümeyye; Sarıkaya, Mehmet ZekiIn this study, we establish some Hermite-Hadamard type inequalities for functions whose second derivatives absolute value are convex. In accordance with this purpose, we obtain an identity using Green's function. Then using this equality we get our main results.Öğe On New Generalized Fractional Integral Operators and Related Fractional Inequalities(Mehmet Zeki SARIKAYA, 2020) Tunç, Tuba; Budak, Hüseyin; Usta, Fuat; Sarıkaya, Mehmet ZekiIn this paper, we define the generalized $k$-fractional integrals of a function with respect to the another function which generalizes many different types of fractional integrals such as Riemann-Liouville fractional, Hadamard fractional integrals, Katugampola fractional integral, $(k,s)$-fractional integral operators. Moreover, we obtain Hermite-Hadamard inequalities utilizing $k$-fractional integrals of a function with respect to the another function. We also investigate trapezoid inequalities for the functions whose derivatives in absolute value are convex. Finally, some special cases of these inequalities are given.Öğe PERTURBED COMPANION OF OSTROWSKI TYPE INEQUALITY FOR TWICE DIFFERENTIABLE FUNCTIONS'(Univ Nis, 2016) Sarıkaya, Mehmet Zeki; Budak, Hüseyin; Tunç, Tuba; Erden, Samet; Yaldız, HaticeIn this paper, some perturbed companion of Ostrowski type integral inequalities for functions whose second derivatives are either bounded or of bounded variation are established.Öğe Some Generalized Integral Inequalities for Convex Functions and Applications(Amer Inst Physics, 2016) Sarıkaya, Mehmet Zeki; Tunç, Tuba; Yıldız, Mustafa KemalIn this paper, some new integral inequalities and their applications to special means of real numbers will be given using generalized Hermite-Hadamard's integral inequalities and Simpson's type inequalities holding for convex functions. Our results presented here would provide extensions of those given in earlier works.Öğe SOME GENERALIZED STEFFENSEN'S INEQUALITIES VIA A NEW IDENTITY FOR LOCAL FRACTIONAL INTEGRALS(Etamaths Publ, 2017) Tunç, Tuba; Sarıkaya, Mehmet Zeki; Srivastava, H.M.In this study, we first give an identity for local fractional integrals. We then make use of this identity in order to derive several generalizations of the celebrated Steffensen's inequality associated with local fractional integrals. Relevant connections of the results presented in this paper with those that were proven in earlier works are also pointed out.
