Sobre funciones $\eta$-convexas generalizadas
Resumen
El concepto de función $\eta$-convexa fue recientemente introducido por Gordji et al. \cite{GordjiDS}. Una funci\'on $f:I=[a,b]\subset \mathbb{R}\to \mathbb{R}$ se dice $\eta$-convexa con respecto a una funci\'on $\eta:\mathbb{R}\times\mathbb{R}\to \mathbb{R}$, si \[
f(tx+(1-t)y)\leq f(y)+t \eta(f(x),f(y)),
\]
for all $x,y\in I$ and $t\in[0,1]$.
En este trabajo, introducimos y estudiamos una generalización de las funciones $\eta$-convexas usando el cálculo fractal desarrollado por Yang \cite{Yang}. Entre otros resultados, mostramos que este tipo de funciones satisfacen algunas desigualdades del tipo Hermite-Hadamard y del tipo Fejér.
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Referencias
Awan M. U., Noor M. A., Noor K. I., Safdar F.} (2017) ``On strongly
generalized convex functions''. emph{Filomat} Vol. 31, No. 18, 5783--5790.
Babakhani A., Daftardar-Gejji V.} (2002) ``On calculus of local fractional
derivatives''. emph{Journal of Mathematical Analysis and Applications} Vol. 270, No. 1, 66--79.
Carpinteri A., Chiaia B., Cornetti P.} (2001) ``Static-kinematic duality
and the principle of virtual work in the mechanics of fractal media''. emph{Computer
Methods in Applied Mechanics and Engineering.} Vol. 191, No. 1-2, 3--19.
Chen G. S.} (2012) ``A generalized Young inequality and some new results on fractal space''. emph{Advances in Computational Mathematics and its Applications} Vol. 1, No. 1, 56--59.
Edgar G. A. (1998) ``Integral, Probability, and Fractal Measures''. emph{Springer,
New York, NY, USA}.
Falconer K. (2003) ``Fractal Geometry: Mathematical Foundations and Applications''. emph{John Wiley $&$ Sons, Hoboken, NJ, USA, 2nd edition}.
bibitem{GordjiDS} {sc Gordji M. E., Delavar M. R., Sen M. D. L.} (2016) ``On $varphi$-convex functions''. emph{Journal of Mathematical Inequalities} Vol. 10, No. 1, 173--183.
Mandelbrot B. B.} (1983) ``The Fractal Geometry of Nature''. emph{Macmillan,
New York, NY, USA.}.
Mo H., Sui X., Yu D.} (2014) ``Generalized convex functions
on fractal sets and two related inequalities''
emph{Abstract and Applied Analysis} Vol. 2014, article ID 636751, 7 pages.
Yang X.-J.} (2012) ``Advanced Local Fractional Calculus and Its Applications''. emph{World
Science, New York, NY, USA}.
Yang X.-J.} (2012) ``Expression of generalized Newton iteration method via generalized local fractional Taylor series''. emph{Advances in Computer Science and its Applications} Vol. 1, No. 2, 89--92.
Zhong W., Gao F., Shen X.} (2012) ``Applications of Yang-Fourier transform
to local fractional equations with local fractional derivative and local fractional
integral''. emph{Advanced Materials Research} Vol. 461, 306--310.
