Some new integral inequalities for Lipschitzian functions
This paper is about obtaining some new type of integral inequalities for functions from the Lipschitz class. For this, some new integral inequalities related to the differences between the two different types of integral averages for Lipschitzian functions are obtained. Moreover, applications for some special means as arithmetic, geometric, logarithmic, -logarithmic, harmonic, identric are given.
[1] Hadamard J. (1893). Étude sur les propriétés des fonctions entiéres et en particulier d’une fonction considérée par Riemann, J. Math. Pures Appl., 58 (1893), 171–215
[2] İşcan, İ . (2014). Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6), 935–942.
[3] Kilbas, A.A. Srivastava, H.M. and Trujillo, J.(2006). Theory and applications of fractional differential equations, Elsevier, Amsterdam.
[4] Roberts, A.W. and Varberg, D.E. (1973) Convex Functions. Academic Press, 300pp, New York.
[5] Dragomir, S.S. Cho, Y.J. and Kim, S.S. (2000). Inequalities of Hadamard's type for Lipschitzian mappings and their applications, Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 489-501.
[6] Hwang, S.R. Hsu, K.C. and Tseng, K.L. (2013). Hadamard-type inequalities for Lipschitzian functions in one and two variables with applications, Journal of Mathematical Analysis and Applications, vol. 405, no. 2, 546-554.
[7] İşcan, İ . (2014). New general integral inequalities for Lipschitzian functions via Hadamard fractional integrals, International Journal of Analysis, volume 2014, Article ID 353924, 8 pages.
[8] İşcan, İ . (2016). Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 4 (1), 77-87.