The main aim of the present paper is to introduce geodesic (E, F)-convex sets and geodesic (E, F)-functions on a Riemannian manifold. Furthermore, some basic properties of these mappings are investigated. Moreover, the Hadamard-type inequalities for (E, F)-convex functions are proven.
Keywords: ($$, $$)-convex functions, geodesic convex functions, geodesic convex sets, geodesic $$-convex functions, Riemannian manifolds
@article{RO_2022__56_6_4181_0,
author = {Saleh, Wedad},
title = {Hermite{\textendash}Hadamard type inequality for $( E , F )$-convex functions and geodesic ($( E , F )$-convex functions},
journal = {RAIRO. Operations Research},
pages = {4181--4189},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {6},
doi = {10.1051/ro/2022185},
mrnumber = {4520672},
zbl = {1546.26008},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2022185/}
}
TY - JOUR AU - Saleh, Wedad TI - Hermite–Hadamard type inequality for $( E , F )$-convex functions and geodesic ($( E , F )$-convex functions JO - RAIRO. Operations Research PY - 2022 SP - 4181 EP - 4189 VL - 56 IS - 6 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2022185/ DO - 10.1051/ro/2022185 LA - en ID - RO_2022__56_6_4181_0 ER -
%0 Journal Article %A Saleh, Wedad %T Hermite–Hadamard type inequality for $( E , F )$-convex functions and geodesic ($( E , F )$-convex functions %J RAIRO. Operations Research %D 2022 %P 4181-4189 %V 56 %N 6 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2022185/ %R 10.1051/ro/2022185 %G en %F RO_2022__56_6_4181_0
Saleh, Wedad. Hermite–Hadamard type inequality for $( E , F )$-convex functions and geodesic ($( E , F )$-convex functions. RAIRO. Operations Research, Tome 56 (2022) no. 6, pp. 4181-4189. doi: 10.1051/ro/2022185
[1] , On some generalization of convex sets, convex functions, and convex optimization problems. M.Sc. thesis, , Department of Mathematics, College of Education Ibn AL-Haitham, University of Baghdad, Iraq (2018).
[2] and , Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels. Math. Methods Appl. Sci. 44 (2021) 8431–8414. | MR | Zbl | DOI
[3] and , Strong geodesic convex functions of order . Numer. Funct. Anal. Optim. 40 (2019) 1840–1846. | MR | Zbl | DOI
[4] , and , On geodesic -convex sets, geodesic -convex functions and -epigraphs. J. Optim. Theory Appl. 55 (2012) 239–251. | MR | Zbl | DOI
[5] , On generalized convexity. Int. J. Math. Sci. 2 (2003) 121–132. | MR | Zbl
[6] , Incorrect results for -convex functions and -convex programming. Math. Res. Exposition 23 (2003) 461–466. | MR | Zbl
[7] , , , , and , New generalized class of convex functions and some related integral inequalities. Symmetry 14 (2022) 722. | DOI
[8] and , On geodesic strongly -convex sets and geodesic strongly -convex functions. J. Inequalities App. 2015 (2015) 1–10. | MR | Zbl
[9] , On strongly E-convex sets and strongly E-convex cone sets. J. AL-Qadisiyah Comput. Sci. Math. 11 (2019) 52–59.
[10] and , On convex functions, E-convex functions and their generalizations: applications to non-linear optimization problems. Int. J. Pure Appl. Math. 116 (2017) 655–673.
[11] , Smooth Nonlinear Optimization in . Vol. 19. Springer Science and Business Media (2013). | MR | Zbl
[12] , , , , and , Hadamard-Mercer, Dragomir–Agarwal–Mercer, and Pachpatte-Mercer type fractional inclusions for convex functions with an exponential kernel and their applications. Symmetry 14 (2022) 836. | DOI
[13] , Some properties of geodesic strongly Eb-vex functions. Int. J. Anal. App. 17 (2019) 388–395. | Zbl
[14] , On some characterizations of -convex functions in the fourth sense. J. Contemporary Appl. Math. 12 (2022) 1–30. | Zbl
[15] and , On Hermite-Hadamard type integral inequalities for strongly -convex functions. Preprint (2012). | arXiv | MR
[16] , and , Some results on φ-convex functions and geodesic φ-convex functions. Differ. Geom.-Dyn. Syst. 20 (2018) 159–169. | MR | Zbl
[17] , -convexity and its generalizations. Int. J. Comput. Math. 88 (2011) 3335–3349. | MR | Zbl | DOI
[18] , , , and , Hermite-Hadamard type inequalities for interval-valued preinvex functions via fractional integral operators. Int. J. Comput. Intell. Syst. 15 (2022) 1–12. | DOI
[19] , and , -convex and related functions. Int. J. Manage. Syst. 102 (2002) 439–450.
[20] and , Some properties of -convex functions. Appl. Math. Lett. 18 (2005) 1074–1080. | MR | Zbl | DOI
[21] , Convex Funcions and Optimization Methods on Riemannian Manifolds. Kluwer Academic (1994). | MR | Zbl | DOI
[22] , -convex sets, -convex functions, and -convex programming. J. Optim. Theory App. 102 (1999) 439–450. | MR | Zbl | DOI
[23] , , and , An improvement of the power-mean integral inequality in the frame of fractal space and certain related midpoint-type integral inequalities. FRACTALS (fractals) 30 (2022) 1–23. | Zbl
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