Scopus İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651
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Article On the Generalized Hermite-Hadamard Inequalities via the Tempered Fractional Integrals(MDPI AG, 2020) Baleanu, Dumitru; Mohammed, Pshtiwan Othman; Sarikaya, Mehmet ZekiArticle Citation - WoS: 24Citation - Scopus: 28New Discrete Inequalities of Hermite-Hadamard Type for Convex Functions(Springer, 2021) Alqudah, Manar A.; Jarad, Fahd; Mohammed, Pshtiwan Othman; Abdeljawad, ThabetWe introduce new time scales on Z. Based on this, we investigate the discrete inequality of Hermite-Hadamard type for discrete convex functions. Finally, we improve our result to investigate the discrete fractional inequality of Hermite-Hadamard type for the discrete convex functions involving the left nabla and right delta fractional sums.Article Citation - WoS: 21Citation - Scopus: 28General Raina Fractional Integral Inequalities on Coordinates of Convex Functions(Springer, 2021) Kashuri, Artion; Mohammed, Pshtiwan Othman; Meftah, Badreddine; Baleanu, DumitruIntegral inequality is an interesting mathematical model due to its wide and significant applications in mathematical analysis and fractional calculus. In this study, authors have established some generalized Raina fractional integral inequalities using an (l1,h1)-(l2,h2)-convex function on coordinates. Also, we obtain an integral identity for partial differentiable functions. As an effect of this result, two interesting integral inequalities for the (l1,h1)-(l2,h2)-convex function on coordinates are given. Finally, we can say that our findings recapture some recent results as special cases.Article Citation - WoS: 10Citation - Scopus: 12Fuzzy-Interval Inequalities for Generalized Convex Fuzzy-Interval Functions Via Fuzzy Riemann Integrals(Amer inst Mathematical Sciences-aims, 2022) Srivastava, Hari Mohan; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Jawa, Taghreed M.; Khan, Muhammad BilalThe objective of the authors is to introduce the new class of convex fuzzy-interval-valued functions (convex-FIVFs), which is known as p-convex fuzzy-interval-valued functions (p-convex-FIVFs). Some of the basic properties of the proposed fuzzy-interval-valued functions are also studied. With the help of p-convex FIVFs, we have presented some Hermite-Hadamard type inequalities (H-H type inequalities), where the integrands are FIVFs. Moreover, we have also proved the Hermite-Hadamard-Fejer type inequality (H-H Fejer type inequality) for p-convex-FIVFs. To prove the validity of main results, we have provided some useful examples. We have also established some discrete form of Jense's type inequality and Schur's type inequality for p-convex-FIVFs. The outcomes of this paper are generalizations and refinements of different results which are proved in literature. These results and different approaches may open new direction for fuzzy optimization problems, modeling, and interval-valued functions.Article Citation - WoS: 7Citation - Scopus: 7Fractional Integral Inequalities for Exponentially Nonconvex Functions and Their Applications(Mdpi, 2021) Kashuri, Artion; Mohammed, Pshtiwan Othman; Baleanu, Dumitru; Hamed, Y. S.; Srivastava, Hari MohanIn this paper, the authors define a new generic class of functions involving a certain modified Fox-Wright function. A useful identity using fractional integrals and this modified Fox-Wright function with two parameters is also found. Applying this as an auxiliary result, we establish some Hermite-Hadamard-type integral inequalities by using the above-mentioned class of functions. Some special cases are derived with relevant details. Moreover, in order to show the efficiency of our main results, an application for error estimation is obtained as well.Article Citation - WoS: 93Citation - Scopus: 113On the Generalized Hermite-Hadamard Inequalities Via the Tempered Fractional Integrals(Mdpi, 2020) Sarikaya, Mehmet Zeki; Baleanu, Dumitru; Mohammed, Pshtiwan OthmanIntegral inequality plays a critical role in both theoretical and applied mathematics fields. It is clear that inequalities aim to develop different mathematical methods (numerically or analytically) and to dedicate the convergence and stability of the methods. Unfortunately, mathematical methods are useless if the method is not convergent or stable. Thus, there is a present day need for accurate inequalities in proving the existence and uniqueness of the mathematical methods. Convexity play a concrete role in the field of inequalities due to the behaviour of its definition. There is a strong relationship between convexity and symmetry. Which ever one we work on, we can apply to the other one due to the strong correlation produced between them especially in recent few years. In this article, we first introduced the notion of lambda-incomplete gamma function. Using the new notation, we established a few inequalities of the Hermite-Hadamard (HH) type involved the tempered fractional integrals for the convex functions which cover the previously published result such as Riemann integrals, Riemann-Liouville fractional integrals. Finally, three example are presented to demonstrate the application of our obtained inequalities on modified Bessel functions and q-digamma function.