Yazar "Mohammed, Pshtiwan Othman" seçeneğine göre listele

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    Hermite-Hadamard type inequalities for F-convex function involving fractional integrals
    (Springeropen, 2018) Mohammed, Pshtiwan Othman; Sarıkaya, Mehmet Zeki
    In this study, the family F and F-convex function are given with its properties. In view of this, we establish some new inequalities of Hermite-Hadamard type for differentiable function. Moreover, we establish some trapezoid type inequalities for functions whose second derivatives in absolute values are F-convex. We also show that through the notion of F-convex we can find some new Hermite-Hadamard type and trapezoid type inequalities for the Riemann-Liouville fractional integrals and classical integrals.
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    On generalized fractional integral inequalities for twice differentiable convex functions
    (Elsevier, 2020) Mohammed, Pshtiwan Othman; Sarıkaya, Mehmet Zeki
    In this article, some new generalized fractional integral inequalities of midpoint and trapezoid type for twice differentiable convex functions are obtained. In view of this, we obtain new integral inequalities of midpoint and trapezoid type for twice differentiable convex functions in a form classical integral and Riemann-Liouville fractional integrals. Finally, we apply our new inequalities to construct inequalities involving moments of a continuous random variable. (C) 2020 The Author(s). Published by Elsevier B.V.
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    On the Generalized Hermite-Hadamard Inequalities via the Tempered Fractional Integrals
    (Mdpi, 2020) Mohammed, Pshtiwan Othman; Sarıkaya, Mehmet Zeki; Baleanu, Dumitru
    Integral 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.