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Geodesic r -preinvex functions on Riemannian manifolds

Khan, Meraj ; Ahmad, Izhar ; Al-Solamy, Falleh

Journal of Inequalities and Applications, 2014, Vol.2014(1), pp.1-11 [Periódico revisado por pares]

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  • Título:
    Geodesic r -preinvex functions on Riemannian manifolds
  • Autor: Khan, Meraj ; Ahmad, Izhar ; Al-Solamy, Falleh
  • Assuntos: invex sets ; preinvex functions ; -invexity ; Riemannian manifolds
  • É parte de: Journal of Inequalities and Applications, 2014, Vol.2014(1), pp.1-11
  • Descrição: In this article, we introduce a new class of functions called r -invexity and geodesic r -preinvexity functions on a Riemannian manifolds. Further, we establish the relationships between r -invexity and geodesic r -preinvexity on Riemannian manifolds. It is observed that a local minimum point for a scalar optimization problem is also a global minimum point under geodesic r -preinvexity on Riemannian manifolds. In the end, a mean value inequality is extended to a Cartan-Hadamard manifold. The results presented in this paper extend and generalize the results that have appeared in the literature. 58E17, 90C26.
  • Idioma: Inglês

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