Jensen m-Convexity on Set-Valued Function

Eko Dedi Pramana, Ratno Bagus Edy Wibowo, Mohamad Muslikh

Abstract


This paper discusses the class of Jensen m-convex functions and their properties, leading to enhancements of these functions and Jensen's inequalities for set-valued functions. It provides several characterizations and explores various algebraic properties. Additionally, it introduces a discrete Jensen-type inclusion.


Keywords


Jensen m-convex; Jensen-type inclusion; Jensen m-convex set; Set-valued function

Full Text:

PDF

References


J. R. Dwilewicz, "A short history of Convexity," Differential Geometry - Dynamical Systems, vol. 11, pp. 112-129, 2009.

S. S. Dragomir and G. Toader, "Some Inequalities for m-Convex Functions.," Studia Univ. Babes-Bolyai, Math, vol. 38, no. 1, pp. 21-28, 1993.

S. S. Dragomir, "On some new inequalities of Hermite-Hadamard type for m-convex functions," Tamkang J. of Math, vol. 33, no. 1, pp. 45-55, 2002.

L. Hormander, Notions of Convexity, vol. 207, Basel: Birkhäuser, 1994.

M. K. Bakula, M. E. Ozdemir and J. Pecaric, "Hadamard Type Inequalities For m-Convex and (α,m)-Convex," Journal of Inequalities in Pure and Applied Mathematics, vol. 9, no. 4, pp. 96-108, 2008.

T. Lara, N. Marentes, R. Quintero and E. Rosales, "On m-Convexity of Set-Valued Functions," Advances in Operator Theory, vol. 4, no. 1, pp. 1-16, 2019.

T. Lara, N. Marentes, R. Quintero and E. Rosales, "Strong m-Convexity of Set-Valued Functions," Annales Mathematicae Silesianae, vol. 37, pp. 1-13, 2023.

D. Zhang, C. Guo, D. Chen and G. Wang, "Jensen's inequalities for set-valued and fuzzy set-valued functions," Fuzzy Sets and Systems, vol. 404, pp. 178-204, 2021.

S. I. Bradanović, "Improvements of Jensen's inequality and its converse for strongly convex functions with applications to strongly f-divergences," Journal of Mathematical Analysis and Applications, vol. 531, no. 2, p. 127866, 2024.

T. Lara, E. Rosales and J. Sanchez, "New properties of m-convex functions," International Journal of Mathematical Analysis, vol. 9, no. 15, pp. 735-742, 2015.

L. Berbesi, T. Lara, P. Pena and E. Rosales, "On operator m-convex functions in hilbert space," UPI Journal of Mathematics and Biostatistics, vol. 1, no. 2, pp. 1-12, 2018.

T. Lara, N. Marentes, Z. Pales and R. Quintero, "On m-convexity on real linear spaces," UPI Journal of Mathematics and Biostatistics, vol. 1, no. 2, pp. 1-16, 2018.

T. Lara, N. Marentes, R. Quintero and E. Rosales, "On m-concave functions on real linear spaces," Boletin de la Asociacion Matematica Venezolana, vol. 23, no. 2, pp. 131-137, 2016.

T. Lara, N. Marentes, R. Quintero and E. Rosales, "Stability of m-jensen functional equations," Journal of Advances in Mathematics and Computer Science, vol. 24, no. 1, pp. 1-12, 2017.

T. Lara, R. Quintero, E. Rosales and J. Sanchez, "On Strongly Jensen m-Convex Function," Pure Mathematical Sciences, vol. 6, no. 1, pp. 87-94, 2017.

T. Lara, R. Quintero, E. Rosales and J. Sanchez, "On a generalization of the class of Jensen convex functions," Aequationes Mathematicae, vol. 90, 2016.




DOI: https://doi.org/10.18860/ca.v9i2.26901

Refbacks

  • There are currently no refbacks.


Copyright (c) 2024 Eko Dedi Pramana, Ratno Bagus Edy Wibowo, Mohamad Muslikh

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Editorial Office
Mathematics Department,
Universitas Islam Negeri Maulana Malik Ibrahim Malang
Gajayana Street 50 Malang, East Java, Indonesia 65144
Faximile (+62) 341 558933
e-mail: cauchy@uin-malang.ac.id

Creative Commons License
CAUCHY: Jurnal Matematika Murni dan Aplikasi is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.