Some properties of geodesic $(\alpha,E)$-preinvex functions on a Riemannian manifold

Absos Ali Shaikh Chandan Kumar Mondal; Ravi P Agarwal

Some properties of geodesic $(\alpha,E)$-preinvex functions on a Riemannian manifold

Differential Geometry 2019-08-05 v2

Authors: Absos Ali Shaikh Chandan Kumar Mondal , Ravi P Agarwal

Abstract

In this article, we have introduced the concept of \textit{geodesic $(\alpha,E)$ -invex set} and by using this concept the notion of \textit{geodesic $(\alpha,E)$ -preinvex functions} and \textit{geodesic $(\alpha,E)$ -invex functions} are developed on a Riemannian manifold. Moreover, several properties and results are deduced within aforesaid functions. An example is also constructed to illustrate the definition of geodesic $(\alpha,E)$ -invex set. We have also established an important relation between geodesic $(\alpha,E)$ -preinvex function and geodesic $(\alpha,E)$ -invex function in a complete Riemannian manifold.

Keywords

riemannian manifold geodesic $(\alpha,e)$-invex set geodesic $(\alpha,e)$-preinvex function geodesic $(\alpha,e)$-invex function complete riemannian manifold

Cite

@article{arxiv.1905.08182,
  title  = {Some properties of geodesic $(\alpha,E)$-preinvex functions on a Riemannian manifold},
  author = {Absos Ali Shaikh Chandan Kumar Mondal and Ravi P Agarwal},
  journal= {arXiv preprint arXiv:1905.08182},
  year   = {2019}
}

Comments

13 pages, We highly appreciate valuable comments from the interested researchers

Some properties of geodesic $(\alpha,E)$-preinvex functions on a Riemannian manifold

Abstract

Keywords

Cite

Comments

Related papers