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

7 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

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

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

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 = "Publisher Copyright: {\textcopyright} 2019 by the authors.",

year = "2019",

doi = "10.3390/MATH7060547",

language = "English",

volume = "7",

journal = "Mathematics",

issn = "2227-7390",

publisher = "Multidisciplinary Digital Publishing Institute (MDPI)",

number = "6",

}

TY - JOUR

T1 - Generalized geodesic convexity on Riemannian manifolds

AU - Ahmad, Izhar

AU - Khan, Meraj Ali

AU - Ishan, Amira A.

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 - https://www.scopus.com/pages/publications/85069934705

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