Generalized geodesic convexity on Riemannian manifolds

Izhar Ahmad; Meraj Ali Khan; Amira A. Ishan

doi:10.3390/MATH7060547

Generalized geodesic convexity on Riemannian manifolds

Izhar Ahmad, Meraj Ali Khan^*, Amira A. Ishan

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.

Original language	English
Article number	547
Journal	Mathematics
Volume	7
Issue number	6
DOIs	https://doi.org/10.3390/MATH7060547
State	Published - 2019

Bibliographical note

Funding Information:
We thank three anonymous referees very much for many valuable remarks and suggestions that definitely improved the final version of the paper. This research was funded by the Deanship of Scientific Research, University of Tabuk, KSA

Publisher Copyright:
© 2019 by the authors.

Keywords

Geodesic log-invex function
Geodesic log-preinvex function
Global minimum
Mean value inequality
Riemannian manifolds

ASJC Scopus subject areas

Mathematics (all)

Access to Document

10.3390/MATH7060547

Cite this

@article{1a243956c0bb4c17b14d07dfa0af0ab4,

title = "Generalized geodesic convexity on Riemannian manifolds",

abstract = "We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.",

keywords = "Geodesic log-invex function, Geodesic log-preinvex function, Global minimum, Mean value inequality, Riemannian manifolds",

author = "Izhar Ahmad and Khan, {Meraj Ali} and Ishan, {Amira A.}",

note = "Funding Information: We thank three anonymous referees very much for many valuable remarks and suggestions that definitely improved the final version of the paper. This research was funded by the Deanship of Scientific Research, University of Tabuk, KSA Publisher Copyright: {\textcopyright} 2019 by the authors.",

year = "2019",

doi = "10.3390/MATH7060547",

language = "English",

volume = "7",

journal = "Mathematics",

issn = "2227-7390",

publisher = "MDPI AG",

number = "6",

}

TY - JOUR

T1 - Generalized geodesic convexity on Riemannian manifolds

AU - Ahmad, Izhar

AU - Khan, Meraj Ali

AU - Ishan, Amira A.

N1 - Funding Information: We thank three anonymous referees very much for many valuable remarks and suggestions that definitely improved the final version of the paper. This research was funded by the Deanship of Scientific Research, University of Tabuk, KSA Publisher Copyright: © 2019 by the authors.

PY - 2019

Y1 - 2019

N2 - We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.

AB - We introduce log-preinvex and log-invex functions on a Riemannian manifold. Some properties and relationships of these functions are discussed. A characterization for the existence of a global minimum point of a mathematical programming problem is presented. Moreover, a mean value inequality under geodesic log-preinvexity is extended to Cartan-Hadamard manifolds.

KW - Geodesic log-invex function

KW - Geodesic log-preinvex function

KW - Global minimum

KW - Mean value inequality

KW - Riemannian manifolds

UR - http://www.scopus.com/inward/record.url?scp=85069934705&partnerID=8YFLogxK

U2 - 10.3390/MATH7060547

DO - 10.3390/MATH7060547

M3 - Article

AN - SCOPUS:85069934705

SN - 2227-7390

VL - 7

JO - Mathematics

JF - Mathematics

IS - 6

M1 - 547

ER -

Generalized geodesic convexity on Riemannian manifolds

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

Fingerprint

Cite this