FRACTIONAL INTEGRAL IDENTITY, ESTIMATION OF ITS BOUNDS AND SOME APPLICATIONS TO TRAPEZOIDAL QUADRATURE RULE
Abstract
The aim of this paper is to introduce a new extension of preinvexity called
exponentially (m; !1; !2; h1; h2)-preinvexity. Some new integral inequalities of HermiteHadamard type for exponentially (m; !1; !2; h1; h2)-preinvex functions via Riemann-Liouville
fractional integral are established. Also, some new estimates with respect to trapezium-type
integral inequalities for exponentially (m; !1; !2; h1; h2)-preinvex functions via general fractional integrals are obtained. We show that the class of exponentially (m; !1; !2; h1; h2)-
preinvex functions includes several other classes of preinvex functions. At the end, some new
error estimates for trapezoidal quadrature formula are provided as well. This results may
stimulate further research in different areas of pure and applied sciences.
exponentially (m; !1; !2; h1; h2)-preinvexity. Some new integral inequalities of HermiteHadamard type for exponentially (m; !1; !2; h1; h2)-preinvex functions via Riemann-Liouville
fractional integral are established. Also, some new estimates with respect to trapezium-type
integral inequalities for exponentially (m; !1; !2; h1; h2)-preinvex functions via general fractional integrals are obtained. We show that the class of exponentially (m; !1; !2; h1; h2)-
preinvex functions includes several other classes of preinvex functions. At the end, some new
error estimates for trapezoidal quadrature formula are provided as well. This results may
stimulate further research in different areas of pure and applied sciences.
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