Trapezoid and Midpoint Type Inequalities for Preinvex Functions via Quantum Calculus
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Dosyalar
Tarih
2021
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Mdpi
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
In this article, we use quantum integrals to derive Hermite-Hadamard inequalities for preinvex functions and demonstrate their validity with mathematical examples. We use the q(x)(2)- quantum integral to show midpoint and trapezoidal inequalities for q(x)(2)-differentiable preinvex functions. Furthermore, we demonstrate with an example that the previously proved Hermite- Hadamard-type inequality for preinvex functions via q(x)(1)-quantum integral is not valid for preinvex functions, and we present its proper form. We use q(x)(1)-quantum integrals to show midpoint inequalities for q(x)(1)-differentiable preinvex functions. It is also demonstrated that by considering the limit q -> 1(-) and eta(x(2), x(1)) = -eta(x(1), x(2)) = x(2), x(1) in the newly derived results, the newly proved findings can be turned into certain known results.
Açıklama
Anahtar Kelimeler
Hermite-Hadamard inequality, q-integral, quantum calculus, preinvex function, trapezoid inequalities, midpoint inequalities, Hermite-Hadamard Inequalities, Integral-Inequalities, Differentiable Mappings, Real Numbers, Convex
Kaynak
Mathematics
WoS Q Değeri
Q1
Scopus Q Değeri
Q2
Cilt
9
Sayı
14
