Korean J. Math.  Vol 27, No 4 (2019)  pp.843-860
DOI: https://doi.org/10.11568/kjm.2019.27.4.843

Some new estimates for exponentially $(\hbar,\mathfrak{m})$-convex functions via extended generalized fractional integral operators

Saima Rashid, Muhammad Aslam Noor, Khalida Inayat Noor

Abstract


In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fej\'{e}r type inequalities for the exponentially $(\hbar,\mathfrak{m})$-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.


Keywords


convex function; exponentially convex function; exponentially (h;m)-convex function; generalized Mittag-Leffler function; generalized fractional integral operators; Hadamard-Fej´er inequality

Subject classification

26D15, 26D10, 90C23

Sponsor(s)



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