ON INTEGRAL INEQUALITIES FOR INVEX FUNCTIONS SATISFYING LIPSCHITZIAN REQUIREMENT

Year 2020, Volume: 3 Issue: 1 , 1 - 10 , 31.01.2020

Seda Kılınç , Abdullah Akkurt , Hüseyin Yildirim

https://doi.org/10.33773/jum.679836

https://izlik.org/JA73EA83XB

Abstract

Some new type of integral inequalities for functions from the Lipschitz class are obtained. These results involve some different types of integral
averages for Lipschitzian functions. Special cases which are naturally included in the main results of the paper are also discussed.

Keywords

Fractional Integral , Riemann-Liouville Fractional Integral , Integral Inequalities

References

• Hadamard J. Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann, J. Math. Pures Appl., 171-215, 58 (1893).
• İşcan, İ. Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics, Volume 43 (6), 935-942, (2014).
• Kilbas, A.A. Srivastava, H.M. and Trujillo, J., Theory and applications of fractional differential equations, Elsevier, Amsterdam (2006).
• Roberts, A.W. and Varberg, D.E. Convex Functions. Academic Press, 300pp, New York (1973).
• Dragomir, S.S. Cho, Y.J. and Kim, S.S., Inequalities of Hadamard's type for Lipschitzian mappings and their applications, Journal of Mathematical Analysis and Applications, vol. 245, no. 2, pp. 489-501, (2000).
• Hwang, S.R. Hsu, K.C. and Tseng, K.L., 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, (2013).
• İşcan, İ. New general integral inequalities for Lipschitzianfunctions via Hadamard fractional integrals, International Journal of Analysis, volume 2014, Article ID 353924, 8 pages, (2014).
• İşcan, İ., Hadamard-type and Bullen-type inequalities for Lipschitzian functions via fractional integrals, Mathematical Sciences and Applications E-Notes, 4 (1), 77-87, (2016).
• Hadamard J. " Etude sur les proprietes des fonctions entieres et en particulier dune fonction consideree par Riemann" , J. Math. Pures Appl., 58 , 171-215, (1893).
• Hanson, M.A., On sufficiency of the Kuhn-Tucker conditions, J. Math. Anal. Appl. 80, 545-550, (1981).
• İşcan, İ., Kadakal, M.,Aydın A., 'Some New integral inequalities for Lipschitzian functions' IJOCTA vol.8, no. 2, pp. 259-265, (2018).
• Kilinc, S., Akkurt, A., and Yıldırım, H., Integral Inequalities for Hypergeometric Operators via Fractional Integral, Journal of Inequalities & Special Functions 8 (5), (2017).
• Noor, M.A., Awan, M.U. and Noor, K.I., On some inequalities for relative semi-convex functions, Journal of Inequalities and Applications, 2013.
• Noor, M.A., Noor, K.I. and Awan, M.U., Hermite-Hadamard inequalities for relative semiconvex functions and applications, Filomat, in press.
• Mohan, S.R., Neogy, S.K., On Invex Sets and Preinvex Functions, Journal of Mathematical Analysis and Applications, 1995.
• Noor, M.A., Awan, M.U., Some Integral inequalities for two senses of convexities via fractional integrals, TJMM 5(2013), no.2, 129-136.