Strongly convexity on fractal sets and some inequalities

Authors

DOI:

https://doi.org/10.22199/issn.0717-6279-2020-01-0001

Keywords:

Convex function, Generalized convex function, Strongly convex function, Fractal set

Abstract

We introduce a generalization of the concept of a strongly convex function on a fractal set, study some algebraic properties and establish Jensen-type and Hermite-Hadamard-type inequalities.

Author Biographies

Rainier V. Sánchez C., Instituto Superior de Formación Docente Salom Ureña.

Departamento de Matemáticas.

José Eduardo Sanabria, Universidad de Sucre.

Departamento de Matemáticas. Facultad de Educación y Ciencias.

References

A. Azócar, J. Giménez, K. Nikodem, and J. L. Sánchez, “On strongly midconvex functions”, Opuscula mathematica, vol. 31, no. 1, pp. 15–26, 2011, doi:10.7494/OpMath.2011.31.1.15.

G.-S. Chen, “A generalized Young inequality and some new results on fractal space”, Jul. 2011. arXiv: 1107.5222v1

K. M. Kolwankar and A. D. Gangal, “Fractional differentiability of nowhere differentiable functions and dimensions”, Chaos, vol. 6, no. 4, pp. 505-513, 1996, doi: 10.1063/1.166197.

T. Lara, N. Merentes, R. Quintero and E. Rosales, “On strongly mconvex functions”, Mathematica aeterna, vol. 5, no. 3, pp. 521-535, 2015. [On line]. Available: https://bit.ly/2G6kHpF

N. Merentes and K. Nikodem, “Remarks on strongly convex functions”, Aequationes mathematicae, vol. 80, no. 1-2, pp. 193-199. 2010, doi: 10.1007/s00010-010-0043-0.

H. Mo, X. Sui and D. Yu, “Generalized convex functions on fractal sets and two related inequalities”, Abstract and applied analysis, Art. ID 636751, 2014, doi: 10.1155/2014/636751.

L. Montrucchio, “Lipschitz policy functions for strongly concave optimization problems”, Journal of mathematical economics, vol. 16, no. 3, pp. 259-273, 1987, doi: 10.1016/0304-4068(87)90012-7.

B. T. Polyak, “Existence theorems and convergence of minimizing sequences in extremum problems with restrictions”, Soviet mathematics. Doklady, vol. 166, no. 2, pp. 72-75, 1966.[On line]. Available: https://bit.ly/2v9BrtX

A. W. Roberts and D. E. Varberg, “Convex functions”, New York, NY: Academic Press, 1973.

W. Sun, “Generalized harmonically convex functions on fractal sets and related Hermite-Hadamard type inequalities”, Journal of nonlinear sciences and applications, vol. 10, no. 11, pp. 5869-5880, 2017, doi: 10.22436/jnsa.010.11.24.

X.-J. Yang, “Advanced local fractional calculus and its applications”, New York, NY: World Science, 2012.

X.-J. Yang, “Expression of generalized newton iteration method via generalized local fractional Taylor series”, Jun. 2012. arXiv:1106.2780v2

Published

2020-02-04

How to Cite

[1]
R. V. Sánchez C. and J. E. Sanabria, “Strongly convexity on fractal sets and some inequalities”, Proyecciones (Antofagasta, On line), vol. 39, no. 1, pp. 1-13, Feb. 2020.

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