en عمومى General پژوهشي Research paper &lrm; <span class="fontstyle0">In this paper we find a characterization type result for (</span><span class="fontstyle2">&eta;</span>_{<span class="fontstyle3">1</span>}<span class="fontstyle2">,&eta;</span>_{<span class="fontstyle3">2</span>}<span class="fontstyle0">)-convex functions. The Fej&eacute;r integral inequality related to (</span><span class="fontstyle2">&eta;</span>_{<span class="fontstyle3">1</span>}<span class="fontstyle2">,&eta;</span>_{<span class="fontstyle3">2</span>}<span class="fontstyle0">)-convex functions is obtained as a generalization of Fej&eacute;r inequality related to the preinvex and </span><span class="fontstyle2">&eta;</span><span class="fontstyle0">-convex functions. Also some Fej&eacute;r trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (</span><span class="fontstyle2">&eta;</span>_{<span class="fontstyle3">1</span>}<span class="fontstyle2">,&eta;</span>_{<span class="fontstyle3">2</span>}<span class="fontstyle0">)-convex.</span> Generalized convex function, Fejér inequality, Trapezoid inequality, Mid-point inequality. 193 210 http://ijmsi.ir/browse.php?a_code=A-10-3794-1&slc_lang=en&sid=1 M. Rostamian Delavar m.rostamian@ub.ac.ir 100319475328460010033 100319475328460010033 Yes Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, Bojnord, Iran S. Mohammadi Aslani soraya.mohammadi.aslani@gmail.com 100319475328460010034 100319475328460010034 No Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran S. M. Vaezpour vaez@aut.ac.ir 100319475328460010035 100319475328460010035 No Department of Mathematics and Computer Sciences, Amirkabir University of Technology, 242 Hafez Ave, Tehran, Iran