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Department of Mathematics, Texas A&M University, Texas
10.22034/kjm.2020.220226.1717
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.
Shaikh, A., Mondal, C., & Agarwal, R. (2021). Some properties of geodesic $(\alpha,E)$-preinvex functions on Riemannian manifolds. Khayyam Journal of Mathematics, 7(2), 201-210. doi: 10.22034/kjm.2020.220226.1717
MLA
Absos Ali Shaikh; Chandan Kumar Mondal; Ravi P. Agarwal. "Some properties of geodesic $(\alpha,E)$-preinvex functions on Riemannian manifolds". Khayyam Journal of Mathematics, 7, 2, 2021, 201-210. doi: 10.22034/kjm.2020.220226.1717
HARVARD
Shaikh, A., Mondal, C., Agarwal, R. (2021). 'Some properties of geodesic $(\alpha,E)$-preinvex functions on Riemannian manifolds', Khayyam Journal of Mathematics, 7(2), pp. 201-210. doi: 10.22034/kjm.2020.220226.1717
VANCOUVER
Shaikh, A., Mondal, C., Agarwal, R. Some properties of geodesic $(\alpha,E)$-preinvex functions on Riemannian manifolds. Khayyam Journal of Mathematics, 2021; 7(2): 201-210. doi: 10.22034/kjm.2020.220226.1717
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