New Hadamard-type inequality for new class of geodesic convex functions
Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 4, p. 276-283.

Voir la notice de l'article provenant de la source International Scientific Research Publications

This paper aims to introduce the concept of ($ E,\mu,\kappa $)-convex function by using special inequality. Hadamard integral inequality for this new class of geodesic convex function in the case of Lebesgue and Sugeno integrals is given.
DOI : 10.22436/jnsa.015.04.03
Classification : 39B62, 31C12, 37D40
Keywords: Convex function, geodesic, Riemannian manifolds

Saleh, W. 1

1 Department of Mathematics, Taibah University, Al-Medina 20012, Saudi Arabia
@article{JNSA_2022_15_4_a2,
     author = {Saleh, W.},
     title = {New {Hadamard-type} inequality for new class of geodesic convex functions},
     journal = {Journal of nonlinear sciences and its applications},
     pages = {276-283},
     publisher = {mathdoc},
     volume = {15},
     number = {4},
     year = {2022},
     doi = {10.22436/jnsa.015.04.03},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.04.03/}
}
TY  - JOUR
AU  - Saleh, W.
TI  - New Hadamard-type inequality for new class of geodesic convex functions
JO  - Journal of nonlinear sciences and its applications
PY  - 2022
SP  - 276
EP  - 283
VL  - 15
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.04.03/
DO  - 10.22436/jnsa.015.04.03
LA  - en
ID  - JNSA_2022_15_4_a2
ER  - 
%0 Journal Article
%A Saleh, W.
%T New Hadamard-type inequality for new class of geodesic convex functions
%J Journal of nonlinear sciences and its applications
%D 2022
%P 276-283
%V 15
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.04.03/
%R 10.22436/jnsa.015.04.03
%G en
%F JNSA_2022_15_4_a2
Saleh, W. New Hadamard-type inequality for new class of geodesic convex functions. Journal of nonlinear sciences and its applications, Tome 15 (2022) no. 4, p. 276-283. doi : 10.22436/jnsa.015.04.03. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.015.04.03/

[1] Abbaszadeh, S.; Ebadian, A. Nonlinear integrals and Hadamard-type inequalities, Soft Comput., Volume 22 (2018), pp. 2843-2849

[2] Abbaszadeh, S.; Oraki, M.; Ebadian, A. Hadamard integral inequality for the class of geodesic convex functions, Appl. Math. Inf. Sci., Volume 15 (2021), pp. 539-546

[3] Abou-Tair, I.; Sulaiman, W. T. Inequalities via convex functions, Int. J. Math. Math. Sci., Volume 22 (1999), pp. 543-546

[4] Chen, X. S. Some properties of semi-$E$-convex functions, J. Math. Anal. Appl., Volume 275 (2002), pp. 251-262 | DOI | Zbl

[5] Duca, D. I.; Lupsa, L. On the E-epigraph of an E-convex functions, J. Optim. Theory Appl., Volume 129 (2006), pp. 341-348

[6] Fulga, C.; Preda, V. Nonlinear programming with E-preinvex and local E-preinvex functions, European J. Oper. Res., Volume 192 (2009), pp. 737-743

[7] Giorgi, G. A Simple Way to Prove the Characterization of Differentiable Quasiconvex Functions, Appl. Math., Volume 5 (2014), pp. 12-26

[8] Goldfarb, D.; Ma, S. Q.; Scheinberg, K. Fast alternating linearization methods for minimizing the sum of two convex functions, Math. Program., Volume 141 (2013), pp. 349-382

[9] Iqbal, A.; Ahmad, I.; Ali, S. Some properties of geodesic semi-$E$-convex functions, Nonlinear Anal., Volume 74 (2011), pp. 6805-6813 | Zbl | DOI

[10] Iqbal, A.; Ali, S.; Ahmad, I. On geodesic $E$-convex sets, geodesic $E$-convex functions and $E$-epigraphs, J. Optim. Theory Appl., Volume 155 (2012), pp. 239-251 | DOI | Zbl

[11] Kılıçman, A.; Saleh, W. On Geodesic Strongly E-convex Sets and Geodesic Strongly E-convex Functions, J. Inequal. Appl., Volume 2015 (2015), pp. 1-10

[12] Kılıçman, A.; Saleh, W. On geodesic semi strongly E-convex functions, J. Interdiscip. Math., Volume 19 (2016), pp. 1039-1055

[13] Kılıçman, A.; Saleh, W. On properties of geodesic semilocal E-preinvex functions, .J. Inequal. Appl., Volume 2018 (2018), pp. 1-13

[14] Noor, M. A. Fuzzy preinvex functions, Fuzzy sets and systems, Volume 64 (1994), pp. 95-104

[15] Noor, M. A.; Awan, M. U.; Noor, K. I. On some inequalities for relative semi-convex functions, J. Inequal. Appl., Volume 2013 (2013), pp. 1-16

[16] Noor, M. A.; K. I. Noor; Awan, M. U. Generalized convexity and integral inequalities, Appl. Math. Inf. Sci., Volume 9 (2015), pp. 233-243

[17] Pap, E. Null-additive set functions, Springer, Berlin, 1995

[18] Pečarić, J. E.; Proschan, F.; Tong, Y. L. Convex functions, partial orderings, and statistical applications, Academic Press, Boston, 1992

[19] Ralescu, D.; Adams, G. The fuzzy integral, J. Math. Anal. Appl., Volume 75 (1980), pp. 562-570

[20] Rapcsak, T. Smooth Nonlinear Optimization in $\mathbb{R}^{n}$, Kluwer Academic Publishers, Dordrecht, 1977

[21] Saleh, W. Some Properties of Geodesic Strongly Eb-vex Functions, Int. J. Anal. Appl., Volume 17 (2019), pp. 388-395

[22] Sugeno, M. Theory of fuzzy integrals and its applications,, Doctoral Thesis, Tokyo Institute of technology, 1974

[23] Syau, Y.-R.; Lee, E. S. Some properties of $E$-convex functions, Appl. Math. Lett., Volume 18 (2005), pp. 1074-1080 | Zbl | DOI

[24] Udrist, C. Convex Funcions and Optimization Methods on Riemannian Manifolds, Kluwer Academic Publishers, Dordrecht, 1994

[25] Vosoughian, H. Hadamard integral inequality for the class of semi-harmonically convex functions, Asian-Eur. J. Math., Volume 15 (2022), pp. 1-21

[26] Wang, Z. Y.; Klir, G. J. Fuzzy measure theory, Plenum Press, New York, 1992

[27] Yang, X. M. On E-convex set, E-convex functions and E-convex programming, J. Optim. Theory Appl., Volume 109 (2001), pp. 699-703

[28] Youness, E. A. $E$-convex sets, $E$-convex functions, and $E$-convex programming, J. Optim. Theory Appl., Volume 102 (1999), pp. 439-450 | DOI | Zbl

[29] Youness, E. A.; Emam, T. Strongly $E$-convex sets and strongly $E$-convex functions, J. Interdiscip. Math., Volume 8 (2005), pp. 107-117 | Zbl | DOI

[30] Youness, E. A.; Emam, T. Semi strongly E-convex functions, J. Math. Stat., Volume 1 (2005), pp. 51-57

[31] Youness, E. A.; Emam, T. Characterization of efficient solutions for multi-objective optimization problems involving semistrong and generalized semi-strong E-convexity, Acta Math. Sci. Ser. B (Engl. Ed.), Volume 28 (2008), pp. 7-16

Cité par Sources :