TY - JOUR AU - Dragomir, S. S. PY - 2017 TI - Generalization and reverses of the left Fejer inequality for convex functions JO - Journal of Nonlinear Sciences and Applications SP - 3231--3244 VL - 10 IS - 6 AB - In this paper we establish a generalization of the left Fej´er inequality for general Lebesgue integral on measurable spaces as well as various upper bounds for the difference \[\frac{1}{\int^b_a g(x)dx} \int^b_ah(x)g(x)dx-h\left(\frac{a+b}{2}\right),\] where \(h : [a, b] \rightarrow \mathbb{R}\) is a convex function and \(g : [a, b] \rightarrow [0,\infty)\) is an integrable weight. Applications for discrete means and Hermite-Hadamard type inequalities are also provided. SN - ISSN 2008-1901 UR - http://dx.doi.org/10.22436/jnsa.010.06.35 DO - 10.22436/jnsa.010.06.35 ID - Dragomir2017 ER - TY - JOUR TI - Convex functions and the Hadamard inequality AU - A. G. Azpeitia JO - Rev. Colombiana Mat. PY - 1994 DA - 1994// VL - 28 ID - Azpeitia1994 ER - TY - BOOK TI - Selected topics on HermiteHadamard inequalities and applications AU - S. S. Dragomir AU - C. E. M. Pearce PB - RGMIA Monographs, Victoria University, Melbourne City PY - 2000 DA - 2000// CY - Australia ID - Dragomir2000 ER - TY - JOUR TI - Über die Fourierreihen, II AU - L. Fejér JO - (Hungarian) Math. Natur. Ungar. Akad Wiss. PY - 1906 DA - 1906// VL - 24 ID - Fejér1906 ER - TY - JOUR TI - Sharp integral inequalities of the Hermite-Hadamard type AU - A. Guessab AU - G. Schmeisser JO - J. Approx. Theory PY - 2002 DA - 2002// VL - 115 ID - Guessab2002 ER - TY - JOUR TI - Hermite-Hadamard’s inequality and the p-HH-norm on the Cartesian product of two copies of a normed space AU - E. Kikianty AU - S. S. Dragomir JO - Math. Inequal. Appl. PY - 2010 DA - 2010// VL - 13 ID - Kikianty2010 ER - TY - JOUR TI - Remarks on Ostrowski’s and Hadamard’s inequality AU - M. Merkle JO - Univ. Beograd. Publ. Elektrotehn. Fak. Ser. Mat. PY - 1999 DA - 1999// VL - 10 ID - Merkle1999 ER - TY - JOUR TI - P-functions, quasi-convex functions, and Hadamard-type inequalities AU - C. E. M. Pearce AU - A. M. Rubinov JO - J. Math. Anal. Appl. PY - 1999 DA - 1999// VL - 240 ID - Pearce1999 ER - TY - JOUR TI - Hadamard and Dragomir-Agarwal inequalities, the Euler formulae and convex functions AU - J. Pečarić AU - A. Vukelić JO - Functional equations, inequalities and applications, Kluwer Acad. Publ., Dordrecht PY - 2003 DA - 2003// VL - ID - Pečarić2003 ER - TY - JOUR TI - Superadditivity and Hermite-Hadamard’s inequalities AU - G. Toader JO - Studia Univ. Babe-Bolyai Math. PY - 1994 DA - 1994// VL - 39 ID - Toader1994 ER - TY - JOUR TI - A note on Hadamard’s inequality AU - G.-S. Yang AU - M.-C. Hong JO - Tamkang J. Math. PY - 1997 DA - 1997// VL - 28 ID - Yang1997 ER - TY - JOUR TI - On certain integral inequalities related to Hermite-Hadamard inequalities AU - G.-S. Yang AU - K.-L. Tseng JO - J. Math. Anal. Appl. PY - 1999 DA - 1999// VL - 239 ID - Yang1999 ER -