New integral inequalities for (s,m)- and ( \alpha ,m)-preinvex functions
Resumen
In this note, we give some estimate of the left hand side of generalizedquadrature formula of Gauss-Jacobi in the cases where $f$ and $\left|f\right| ^{\lambda }$ for $\lambda >1$, are $\left( s,m\right) $- and $
\left( \alpha ,m\right) $-preinvex functions.
Visitas al artículo
Descargas
Referencias
I. Ahmad, Integral inequalities under beta function and preinvex
type functions. SpringerPlus. 5 (2016), no. 1, p. 1-6.
J. Chen and X. Huang, Some integral inequalities via $left(
h-left( alpha ,mright) right) $-logarithmically convexity. J. Comput.
Anal. Appl. 20 (2016), no. 2, 374--380.
I. Iscan, M. Aydin and S. Dikmenoglu, New integral inequalities
via harmonically convex functions. Mathematics and Statistics 3(2015), no.
, 134-140.
A. Kashuri and R. Liko, Hermite-Hadamard type fractional integral
inequalities for generalized $(r,s,m,varphi )$-preinvex functions. European
Journal of Pure and Applied Mathematics. 10 (2017), no. 3, 495-505.
A. Kashuri and R. Liko, Generalizations of Hermite-Hadamard and
Ostrowski type inequalities for $MT_{m}$-preinvex functions. Proyecciones 36
(2017), no. 1, 45--80.
M. A. Latif and M. Shoaib, Hermite-Hadamard type integral
inequalities for differentiable $m$-preinvex and $left( alpha ,mright) $
-preinvex functions. J. Egyptian Math. Soc. 23 (2015), no. 2, 236--241.
W. Liu, New integral inequalities via $left( alpha ,mright) $
-convexity and quasi-convexity. Hacet. J. Math. Stat. 42 (2013), no. 3,
--297.
W. Liu, New integral inequalities involving beta function via
-convexity. Miskolc Math. Notes 15 (2014), no. 2, 585--591.
B. Meftah, Hermite-Hadamard's inequalities for functions whose
first derivatives are $(s,m)$-preinvex in the second sense, JNT, 10 (2016),
--65.
B. Meftah, New integral inequalities via strongly convexity.
Electronic Journal of Mathematical Analysis and Applications. 5(2017), no.
, 266-270.
B. Meftah, New integral inequalities for $s$-preinvex functions.
Int. J. Nonlinear Anal. Appl, 8 (2017), no. 1, 331-336.
M. Muddassar and A. Ali, New integral inequalities through
generalized convex functions. Punjab Univ. J. Math. (Lahore) 46 (2014), no.
, 47--51.
M. A. Noor, K. I. Noor, S. Iftikhar and M. U. Awan, Strongly
generalized harmonic convex functions and integral inequalities. Journal of
Mathematical Analysis. 7 (2016), no. 3, 66--77.
M. A. Noor, K. I. Noor, M. U. Awan and J. Li, On Hermite-Hadamard
inequalities for $h$-preinvex functions. Filomat 28 (2014), no. 7,
--1474.
M. A. Noor, K. I. Noor and S. Iftikhar. Harmonic Beta-Preinvex
Functions and Inequalities. International Journal of Analysis and
Applications, 13(2017), no. 2, 144-160.
M. E. "{O}zdemir, E. Set and M. Alomari, Integral inequalities
via several kinds of convexity. Creat. Math. Inform. 20 (2011), no. 1,
--73.
D. D. Stancu, G. Coman and P. Plaga, Analizu{a} numericu{a}
c{s}i teoria aproximu{a}rii. Vol. II. (Romanian) [Numerical analysis and
approximation theory. Vol. II] Presa Universitaru{a} Clujeanu{a},
Cluj-Napoca, 2002.
T. Weir and B. Mond, Pre-invex functions in multiple objective
optimization. J. Math. Anal. Appl. 136 (1988), no. 1, 29--38.