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Öğe FRACTIONAL HERMITE HADAMARD'S TYPE INEQUALITY FOR THE CO-ORDINATED CONVEX FUNCTIONS(Inst Applied Mathematics, 2020) Tunc, Tuba; Sarikaya, Mehmet Zeki; Yaldiz, HaticeIn this paper, we consider the co-ordinated convex functions and obtain some Hermite-Hadamard type inequalities via Riemann-Liouville fractional integrals. For this purpose, we first prove an supplement al result for two variables. Using this auxiliary result, integral inequalities for the left-hand side of the fractional Hermite-Hadamard type inequality on the coordinates are derived. These represent can be viewed as a refinement of the previously known results.Öğe FRACTIONAL HERMITE-HADAMARD-TYPE INEQUALITIES FOR INTERVAL-VALUED FUNCTIONS(Amer Mathematical Soc, 2020) Budak, Huseyin; Tunc, Tuba; Sarikaya, Mehmet ZekiIn this paper, we define interval-valued right-sided Riemann-Liouville fractional integrals. Later, we handle Hermite-Hadamard inequality and Hermite-Hadamard-type inequalities via interval-valued Riemann-Liouville fractional integrals.Öğe GENERALIZED HERMITE-HADAMARD TYPE INEQUALITIES FOR PRODUCTS OF CO-ORDINATED CONVEX FUNCTIONS(Ankara Univ, Fac Sci, 2020) Budak, Huseyin; Tunc, TubaIn this paper, we think products of two co-ordinated convex functions for the Hermite-Hadamard type inequalities. Using these functions we obtained Hermite-Hadamard type inequalities which are generalizations of some results given in earlier works.Öğe A new approach to Simpson-type inequality with proportional Caputo-hybrid operator(Wiley, 2024) Demir, Izzettin; Tunc, TubaIn this article, we begin by deriving a new identity with the help of twice-differentiable convex functions for the proportional Caputo-hybrid operator. Then, using this newly uncovered identity, we obtain various integral inequalities associated with the Simpson's integral inequality for proportional Caputo-hybrid operator. Moreover, we indicate that the acquired results improve and refine certain existing discoveries in the realm of integral inequalities. Finally, for a better understanding of the newly obtained inequalities, we establish illustrative examples and visualize them through their corresponding graphs.Öğe New Hermite-Hadamard type inequalities on fractal set(Semnan Univ, 2021) Tunc, Tuba; Budak, Huseyin; Usta, Fuat; Sarikaya, Mehmet ZekiIn this study, we present the new Hermite-Hadamard type inequality for functions which are h-convex on fractal set R-alpha (0 < alpha <= 1) of real line numbers. Then we provide the special cases of the result using different type of convex mappings.Öğe New midpoint-type inequalities in the context of the proportional Caputo-hybrid operator(Springer, 2024) Demir, Izzettin; Tunc, TubaFractional calculus is a crucial foundation in mathematics and applied sciences, serving as an extremely valuable tool. Besides, the new hybrid fractional operator, which combines proportional and Caputo operators, offers better applications in numerous fields of mathematics and computer sciences. Due to its wide range of applications, we focus on the proportional Caputo-hybrid operator in this research article. Firstly, we begin by establishing a novel identity for this operator. Then, based on the newfound identity, we establish some integral inequalities that are relevant to the left-hand side of Hermite-Hadamard-type inequalities for the proportional Caputo-hybrid operator. Furthermore, we show how the results improve upon and refine many previous findings in the setting of integral inequalities. Later, we present specific examples together with their related graphs to offer a better understanding of the newly obtained inequalities. Our results not only extend previous studies but also provide valuable viewpoints and methods for tackling a wide range of mathematical and scientific problems.Öğe On a new version of Hermite-Hadamard-type inequality based on proportional Caputo-hybrid operator(Springer, 2024) Tunc, Tuba; Demir, IzzettinIn mathematics and the applied sciences, as a very useful tool, fractional calculus is a basic concept. Furthermore, in many areas of mathematics, it is better to use a new hybrid fractional operator, which combines the proportional and Caputo operators. So we concentrate on the proportional Caputo-hybrid operator because of its numerous applications. In this research, we introduce a novel extension of the Hermite-Hadamard-type inequalities for proportional Caputo-hybrid operator and establish an identity. Then, taking into account this novel generalized identity, we develop some integral inequalities associated with the left-side of Hermite-Hadamard-type inequalities for proportional Caputo-hybrid operator. Moreover, to illustrate the newly established inequalities, we give some examples with the help of graphs.Öğe On new trapezoid and midpoint type inequalities for generalized quantum integrals(Univ Nis, Fac Sci Math, 2024) Budak, Huseyin; Kara, Hasan; Tunc, Tuba; Hezenci, Fatih; Khan, SundasIn this article, by utilizing the functions with bounded second derivatives, we first prove some trapezoid and midpoint type inequalities for generalized quantum integrals which are introduced in the recent papers. Then we establish some new quantum integral inequalities for mappings whose second quantum derivatives are bounded. Moreover, we obtain some new weighted trapezoid and midpoint type inequalities for generalized quantum integrals by using the functions with bounded second derivatives. Finally, we investigate the connections between our results and those in earlier works.Öğe Quantum Ostrowski-type integral inequalities for functions of two variables(Wiley, 2021) Budak, Huseyin; Ali, Muhammad Aamir; Tunc, TubaIn this study, we established some new inequalities of Ostrowski type for the functions of two variables by using the concept of newly defined double quantum integrals. We also revealed that the results presented in this paper are the consolidation and generalization of some existing results on the literature of Ostrowski inequalities.
