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Öğe Bounds for the Error in Approximating a Fractional Integral by Simpson's Rule(Mdpi, 2023) Budak, Hueseyin; Hezenci, Fatih; Kara, Hasan; Sarikaya, Mehmet ZekiDaha fazla Simpson's rule is a numerical method used for approximating the definite integral of a function. In this paper, by utilizing mappings whose second derivatives are bounded, we acquire the upper and lower bounds for the Simpson-type inequalities by means of Riemann-Liouville fractional integral operators. We also study special cases of our main results. Furthermore, we give some examples with graphs to illustrate the main results. This study on fractional Simpson's inequalities is the first paper in the literature as a method.Daha fazla Öğe Conformable fractional versions of Hermite-Hadamard-type inequalities for twice-differentiable functions(Springer, 2023) Hezenci, Fatih; Kara, Hasan; Budak, HuseyinDaha fazla In this paper, new inequalities for the left and right sides of the Hermite-Hadamard inequality are acquired for twice-differentiable mappings. Conformable fractional integrals are used to derive these inequalities. Furthermore, we provide our results by using special cases of obtained theorems.Daha fazla Öğe Fractional Simpson-Type Inequalities for Twice Differentiable Functions(Univ Maragheh, 2023) Budak, Hueseyin; Kara, Hasan; Hezenci, FatihDaha fazla In the literature, several papers are devoted to inequal-ities of Simpson-type in the case of differentiable convex functions and fractional versions. Moreover, some papers are focused on in-equalities of Simpson-type for twice differentiable convex functions. In this research article, we obtain an identity for twice differentiable convex functions. Then, we prove several fractional inequalities of Simpson-type for convex functions.Daha fazla Öğe Generalized fractional Hermite-Hadamard type inclusions for co-ordinated convex interval-valued functions(De Gruyter Poland Sp Z O O, 2022) Vivas-Cortez, Miguel J. J.; Kara, Hasan; Budak, Hüseyin; Ali, Muhammad Aamir; Chasreechai, SaowaluckDaha fazla In this article, we introduce the notions of generalized fractional integrals for the interval-valued functions (IVFs) of two variables. We establish Hermite-Hadamard (H-H) type inequalities and some related inequalities for co-ordinated convex IVFs by using the newly defined integrals. The fundamental benefit of these inequalities is that these can be turned into classical H-H inequalities and Riemann-Liouville fractional H-H inequalities, and new k k -Riemann-Liouville fractional H-H inequalities can be obtained for co-ordinated convex IVFs without having to prove each one separately.Daha fazla Öğe Generalized fractional midpoint type inequalities for co-ordinated convex functions(University of Nis, 2023) Hezenci, Fatih; Budak, Hüseyin; Kara, Hasan; Sarıkaya, Mehmet ZekiDaha fazla In this research paper, we investigate generalized fractional integrals to obtain midpoint type inequalities for the co-ordinated convex functions. First of all, we establish an identity for twice partially differentiable mappings. By utilizing this equality, some midpoint type inequalities via generalized fractional integrals are proved. We also show that the main results reduce some midpoint inequalities given in earlier works for Riemann integrals and Riemann-Liouville fractional integrals. Finally, some new inequalities for k-Riemann-Liouville fractional integrals are presented as special cases of our results. © 2023, University of Nis. All rights reserved.Daha fazla Öğe Generalized Hermite-Hadamard inclusions for a generalized fractional integral(Rocky Mt Math Consortium, 2023) Budak, Hueseyin; Kara, Hasan; Hezenci, FatihDaha fazla We introduce new generalized fractional integrals for interval-valued functions. Then we prove generalized Hermite-Hadamard type inclusions for interval-valued convex functions using these newly defined generalized fractional integrals. We also show that these results generalize several results obtained in earlier works.Daha fazla Öğe Hermite-Hadamard, Trapezoid and Midpoint Type Inequalities Involving Generalized Fractional Integrals for Convex Functions(Univ Maragheh, 2023) Kara, Hasan; Erden, Samet; Budak, HüseyinDaha fazla We first construct new Hermite-Hadamard type in-equalities which include generalized fractional integrals for convex functions by using an operator which generates some significant fractional integrals such as Riemann-Liouville fractional and the Hadamard fractional integrals. Afterwards, Trapezoid and Mid-point type results involving generalized fractional integrals for func-tions whose the derivatives in modulus and their certain powers are convex are established. We also recapture the previous results in the particular situations of the inequalities which are given in the earlier works.Daha fazla Öğe Hermite-Hadamard-Mercer type inclusions for interval-valued functions via Riemann-Liouville fractional integrals(Scientific Technical Research Council Turkey-Tubitak, 2022) Kara, Hasan; Ali, Muhammad Aamir; Budak, HüseyinDaha fazla In this research, we first establish some inclusions of fractional Hermite???Hadamard???Mercer type for interval -valued functions. Moreover, by special cases of our main results, we show that our main results reduce several inclusions obtained in the earlier works.Daha fazla Öğe Hermite-Hadamard-type inequalities for interval-valued coordinated convex functions involving generalized fractional integrals(Wiley, 2021) Kara, Hasan; Ali, Muhammad Aamir; Budak, HuseyinDaha fazla In this paper, we define interval-valued left-sided and right-sided generalized fractional double integrals. We establish inequalities of Hermite-Hadamard like for coordinated interval-valued convex functions by applying our newly defined integrals.Daha fazla Öğe New Extensions of the Parameterized Inequalities Based on Riemann-Liouville Fractional Integrals(Mdpi, 2022) Kara, Hasan; Budak, Hüseyin; Hezenci, FatihDaha fazla In this article, we derive the above and below bounds for parameterized-type inequalities using the Riemann-Liouville fractional integral operators and limited second derivative mappings. These established inequalities generalized the midpoint-type, trapezoid-type, Simpson-type, and Bullen-type inequalities according to the specific choices of the parameter. Thus, a generalization of many inequalities and new results were obtained. Moreover, some examples of obtained inequalities are given for better understanding by the reader. Furthermore, the theoretical results are supported by graphs in order to illustrate the accuracy of each of the inequalities obtained according to the specific choices of the parameter.Daha fazla Öğe New midpoint type inequalities for generalized fractional integral(Univ Tabriz, 2022) Budak, Hüseyin; Kara, Hasan; Kapucu, RabiaDaha fazla In this paper, we first establish two new identities for differentiable function involving generalized fractional integrals. Then, by utilizing these equalities, we obtain some midpoint type inequalities involving generalized fractional integrals for mappings whose derivatives in absolute values are convex. We also give several results as special cases of our main results.Daha fazla Öğe New parameterized inequalities for twice differentiable functions(Univ Nis, Fac Sci Math, 2023) Budak, Hüseyin; Kara, Hasan; Hezenci, Fatih; Sarıkaya, Mehmet ZekiDaha fazla The present paper first establishes that an identity involving generalized fractional integrals is proved for twice differentiable functions by using a parameter. By using this equality, we obtain some parameterized inequalities for the functions whose second derivatives in absolute value are convex. Finally, we show that our main results reduce to trapezoid, midpoint Simpson and Bullen-type inequalities which are proved in earlier published papers.Daha fazla Öğe New Simpson type inequalities for twice differentiable functions via generalized fractional integrals(Amer Inst Mathematical Sciences-Aims, 2022) You, Xue Xiao; Hezenci, Fatih; Budak, Hüseyin; Kara, HasanDaha fazla Fractional versions of Simpson inequalities for differentiable convex functions are extensively researched. However, Simpson type inequalities for twice differentiable functions are also investigated slightly. Hence, we establish a new identity for twice differentiable functions. Furthermore, by utilizing generalized fractional integrals, we prove several Simpson type inequalities for functions whose second derivatives in absolute value are convex.Daha fazla Öğe New version of fractional Simpson type inequalities for twice differentiable functions(Springer, 2021) Hezenci, Fatih; Budak, Huseyin; Kara, HasanDaha fazla Simpson inequalities for differentiable convex functions and their fractional versions have been studied extensively. Simpson type inequalities for twice differentiable functions are also investigated. More precisely, Budak et al. established the first result on fractional Simpson inequality for twice differentiable functions. In the present article, we prove a new identity for twice differentiable functions. In addition to this, we establish several fractional Simpson type inequalities for functions whose second derivatives in absolute value are convex. This paper is a new version of fractional Simpson type inequalities for twice differentiable functions.Daha fazla Öğe Novel results of Milne-type inequalities involving tempered fractional integrals(Springer, 2024) Hezenci, Fatih; Budak, Huseyin; Kara, Hasan; Bas, UmutDaha fazla In this current research, we focus on the domain of tempered fractional integrals, establishing a novel identity that serves as the cornerstone of our study. This identity paves the way for the Milne-type inequalities, which are explored through the framework of differentiable convex mappings inclusive of tempered fractional integrals. The significance of these mappings in the realm of fractional calculus is underscored by their ability to extend classical concepts into more complex, fractional dimensions. In addition, by using the Holder inequality and power-mean inequality, we acquire some new Milne-type inequalities. Moreover, the practicality and theoretical relevance of our findings are further demonstrated through the application of specific cases derived from the theorems.Daha fazla Öğe On extensions of Hermite-Hadamard type inclusions for interval-valued convex functions(Univ Nis, Fac Sci Math, 2023) Kara, Hasan; Budak, Huseyin; Hezenci, FatihDaha fazla In this work, by using weighted Jensen inclusion, we establish some new weighted Hermite- Hadamard type inclusions involving two real parameters for interval-valued convex functions. In addition, some extensions of Hermite-Hadamard inclusion are obtained by special choices of parameters. Moreover, we give some examples to illustrate the main results of this work.Daha fazla Öğe On Fejer Type Inclusions for Products of Interval-Valued Convex Functions(Univ Nis, Fac Sci Math, 2021) Budak, Hüseyin; Kara, Hasan; Erden, SametDaha fazla We first get some new Fejer type inclusions for products of interval-valued convex mappings. The most important feature of our work is that it contains Fejer type inclusions for both interval-valued integrals and interval-valued fractional integrals.Daha fazla Öğe On Fejer type inequalities for co-ordinated hyperbolic rho-convex functions(Amer Inst Mathematical Sciences-Aims, 2020) Kara, Hasan; Budak, Huseyin; Kiris, Mehmet EyupDaha fazla In this study, we first establish some Hermite-Hadamard-Fejer type inequalities for coordinated hyperbolic rho-convex functions. Then, by utilizing these inequalities, we also give some fractional Fejer type inequalities for co-ordinated hyperbolic rho-convex functions. The inequalities obtained in this study provide generalizations of some result given in earlier works.Daha fazla Öğe On Fractional Newton Inequalities via Coordinated Convex Functions(Mdpi, 2022) Kösem, Pınar; Kara, Hasan; Budak, Hüseyin; Ali, Muhammad Aamir; Nonlaopon, KamsingDaha fazla In this paper, firstly, we present an integral identity for functions of two variables via Riemann-Liouville fractional integrals. Then, a Newton-type inequality via partially differentiable coordinated convex mappings is derived by taking the absolute value of the obtained identity. Moreover, several inequalities are obtained with the aid of the Holder and power mean inequality. In addition, we investigate some Newton-type inequalities utilizing mappings of two variables with bounded variation. Finally, we gave some mathematical examples and their graphical behavior to validate the obtained inequalities.Daha fazla Öğe On generalized Ostrowski, Simpson and Trapezoidal type inequalities for co-ordinated convex functions via generalized fractional integrals(Springer, 2021) Budak, Huseyin; Hezenci, Fatih; Kara, HasanDaha fazla In this study, we prove an identity for twice partially differentiable mappings involving the double generalized fractional integral and some parameters. By using this established identity, we offer some generalized inequalities for differentiable co-ordinated convex functions with a rectangle in the plane R2. Furthermore, by special choice of parameters in our main results, we obtain several well-known inequalities such as the Ostrowski inequality, trapezoidal inequality, and the Simpson inequality for Riemann and Riemann-Liouville fractional integrals.Daha fazla

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