Sandwich theorem for reciprocally strongly convex functions
- Mireya Bracamonte
- Jesús Medina Moreno
- José Giménez
ISSN: 0034-7426
Año de publicación: 2018
Volumen: 52
Número: 2
Páginas: 171-184
Tipo: Artículo
Otras publicaciones en: Revista Colombiana de Matemáticas
Referencias bibliográficas
- M. Avriel, W.T. Diewert, S. Schaible, and I. Zang, Generalized concavity, 1998.
- K. Baron, J. Matkowski, and K. Nikodem, A sandwich with convexity, Math. Pannica 5/1 (1994), 139–144.
- M. Bessenyei and Zs. Páles, Characterization of convexity via Hadamard's inequality, Math. Inequal. Appl. 9 (2006), 53–62.
- M. Bracamonte, J. Giménez, and J. Medina, Hermite-Hadamard and Fejér type inequalities for strongly harmonically convex functions, Submitted for publication (2016).
- M. Bracamonte, J. Giménez, J. Medina, and M. Vivas, A sandwich theorem and stability result of Hyers-Ulam type for harmonically convex functions, Submitted for publication (2016).
- A. Daniilidis and P. Georgiev, Approximately convex functions and approximately monotonic operators, Nonlin. Anal., 66 (2007), 547–567.
- S. Dragomir, Inequalities of Hermite-Hadamard type for h-convex functions on linear spaces, Mathematica Moravica (2015), 107–121.
- S. Dragomir, Inequalities of Jensen type for HA-convex functions, RGMIA Monographs, Victoria University (2015).
- S. Dragomir and C. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, 2000.
- A. Eberhard and Pearce C. E. M., Class inclusion properties for convex functions, in progress in optimization, Appl. Optim, Kluwer Acad. Publ., Dordrecht, 39 (1998), 129–133. [11] L. Fejér, Über die fourierreihen, II, Math. Naturwiss. Anz Ungar. Akad.Wiss. (1906), 369–390.
- A. Ghazanfari and S. Dragomir, Hermite-Hadamard inequality for functions whose derivatives absolute values are preinvex, 2012.
- G.H. Hardy, J.E. Littlewood, and G. Polya, Inequalities, Cambridge Univ. Press., 1934.
- J. Hiriart-Urruty and C. Lemaréchal, Fundamentals of convex analysis, Springer-Verlag, Berlin-Heidelberg, 2001.
- D. H. Hyers, On the stability of the linear functional equations, Proc. Nat. Acad. Sci. USA 27 (1941), 222–224.
- D. H. Hyers and S. M. Ulam, Approximately convex functions, Proc. Amer. Math. Soc.3 (1952), 821–828.
- I. Iscan, Hermite-Hadamard type inequalities for harmonically (α,m) convex functions, Contemp. Anal. Appl. Math., 1 (2) (2013), 253–264.
- I. Iscan, New estimates on generalization of some integral inequalities for s-convex functions and their applications, Int. J. Pure Appl. Math., 86 (4) (2013), 727–726.
- I. Iscan, Hermite-Hadamard type inequalities for harmonically convex functions, Hacettepe Journal of Mathematics and Statistics Volume 43 (6) (2014), 935 – 942.
- M.V. Jovanovic, A note on strongly convex and strongly quasiconvex functions, Notes 60 (1996), 778–779.
- S.M. Jung, Hyers-ulam-rassias stability of functional equations in mathematical analysis, Hadronic Press, Inc., Palm Harbor, 2001.
- M. Kuczma, An introduction to the theory of functional equations and inequalities, Cauchy's equation and Jensen's inequality, Second Edition, Birkhäuser, Basel Boston Berlin, 2009.
- N. Merentes and K. Nikodem, Remarks on strongly convex functions, Aequationes mathematicae,Volume 80, Issue 1 (2010), 193–199.
- F. C. Mitroi-Symeonidis, Convexity and sandwich theorems, European Journal of Research in Applied Sciences, Vol. 1, No. 1 (2015), 9–11.
- C. Niculescu and L. Persson, Convex functions and their applications, A Contemporary Approach, CMS Books in Mathematics, vol. 23, Springer, New York, 2006.
- K. Nikodem and S. Wa¸sowicz, A sandwich theorem and Hyers-Ulam stability of affine functions, Aequationes Math. 49 (1995), 160–164.
- M. A. Noor, K. I. Noor, and M. U. Awan, Some characterizations of harmonically log-convex functions, Proc. Jangjeon Math. Soc., 17(1) (2014), 51–61.
- M. A. Noor, K. I. Noor, and M. U. Awan, Some integral inequalities for harmonically logarithmic h-convex functions, preprint (2014).
- B. Polyak, Existence theorems and convergence of minimizing sequences in extremum problems with restrictions, Dokl. Akad. Nauk. SSSR 166 (1966), 287–290.
- A. Roberts and D. Varberg, Convex functions, Academic Press, New York-London, 1973.
- R.T. Rockafellar, Monotone operator and the proximal point algorithm, SIAM J. Control Optim 14 (1976), 888–898.
- S.M. Ulam, A collection of mathematical problems, Interscience Publ., New York, 1960.
- S. Varosanec, On h-convexity, J. Math. Anal. Appl. 326 (2007), 303 – 311.
- T.-Y Zhang, A.-P. Ji, and F. Qi, Integral inequalities of Hermite-Hadamard type for harmonically quasiconvex functions, Proc. Jangjeon Math. Soc., 16(3) (2013), 399–407.