Affiliations 

  • 1 1Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, Serdang, Malaysia
  • 2 2Department of Mathematics, Taibah University, Al-Medina, Saudi Arabia
J Inequal Appl, 2018;2018(1):353.
PMID: 30839923 DOI: 10.1186/s13660-018-1944-z

Abstract

The authors define a class of functions on Riemannian manifolds, which are called geodesic semilocal E-preinvex functions, as a generalization of geodesic semilocal E-convex and geodesic semi E-preinvex functions, and some of its properties are established. Furthermore, a nonlinear fractional multiobjective programming is considered, where the functions involved are geodesic E-η-semidifferentiability, sufficient optimality conditions are obtained. A dual is formulated and duality results are proved by using concepts of geodesic semilocal E-preinvex functions, geodesic pseudo-semilocal E-preinvex functions, and geodesic quasi-semilocal E-preinvex functions.

* Title and MeSH Headings from MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine.