On Generalization of Fejer Type Inequalities

Mohsen Rostamian Delavar, M. De La Sen

Abstract


Some generalizations of Fejér type inequalities related to \(\eta\)-convex functions are investigated. Also applications for trapezoid and mid-point type inequalities are given.

Keywords


\(\eta\)-convex function; Hermite-Hadamard-Fejér inequality; Trapezoid and mid-point type inequality

Full Text:

PDF

References


M. Bombardelli and S. Varosanec, Properties of h-convex functions related to the Hermite-Hadamard-Fejér inequalities, Comput. Math. Appl. 58 (9) (2009), 1869 – 1877.

S. S. Dragomir and R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett. 11 (1998), 91 – 95.

M. Eshaghi Gordji, S. S. Dragomir and M. Rostamian Delavar, An inequality related to (varphi)-convex functions (II), Int. J. Nonlinear Anal. Appl. 6 (2) (2016), 26 – 32.

M. Eshaghi Gordji, M. Rostamian Delavar and M. De La Sen, On '-convex functions, J. Math. Inequal. 10 (1) (2016), 173 – 183.

L. Fejér, Über die fourierreihen, II, Math. Naturwise. Anz Ungar. Akad. Wiss. 24 (1906), 369 – 390.

S.-R. Hwang, K.-L. Tseng and K.-C. Hsu, Hermite-Hadamard type and Fejér type inequalities for general weights (I), J. Inequal. Appl. 2013: 170, 13 p.

U. S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 147 (1) (2004), 137 – 146.

B. Micherda and T. Rajba, On Some Hermite-Hadamard-Fejér inequalities for (k,h)-convex function, Math. Inequal. Appl. 4 (2012), 931 – 940.

J. Park, Inequalities of Hermite-Hadamard-Fejér type for convex functions via fractional integrals, International Journal of Mathematical Analysis 8 (59) (2014), 2927 – 2937.

M. Rostamian Delavar and S. S. Dragomir, On (eta)-convexity, Math. Inequal. Appl. 20 (2017), 203 – 216.

K.-L. Tseng, S.-R. Hwang and S. S. Dragomir, Fejér-type inequalities (I), J. Inequal. Appl. 239 (2010), Article ID 531976, 7 p.

G.-S. Yang, Inequalities of Hadamard’s type for Lipschitzian mappings, J. Math. Anal. Appl. 260 (2001), 230 – 238.


Refbacks

  • There are currently no refbacks.


eISSN 0975-8607; pISSN 0976-5905