On the Generalized Hermite-Hadamard Inequalities via the Tempered Fractional Integrals
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Dosyalar
Tarih
2020
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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.
Açıklama
Anahtar Kelimeler
Hermite-Hadamard inequality, incomplete gamma functions, fractional integrals, Differentiable Mappings, Convex-Functions, Real Numbers
Kaynak
Symmetry-Basel
WoS Q DeÄŸeri
Q2
Scopus Q DeÄŸeri
Q2
Cilt
12
Sayı
4
