Characterizations of geodesic sub-\(b\)-\(s\)-convex functions on Riemannian manifolds
Volume 11, Issue 2, pp 189--197
http://dx.doi.org/10.22436/jnsa.011.02.02
Publication Date: January 21, 2018
Submission Date: April 10, 2017
Revision Date: December 04, 2017
Accteptance Date: December 06, 2017
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Authors
Izhar Ahmad
- Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia.
Anurag Jayswal
- Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India.
Babli Kumari
- Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad-826004, Jharkhand, India.
Abstract
In this paper, we present the notion of geodesic sub-\(b\)-\(s\)-convex function on the Riemannian manifolds. A non-trivial example of geodesic sub-\(b\)-\(s\)-convex function but not geodesic convex function is also discussed. Some fundamental properties of geodesic sub-\(b\)-\(s\)-convex functions are investigated. Moreover, we derive the optimality conditions of unconstrained and constrained programming problems under the sub-\(b\)-\(s\)-convexity.
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ISRP Style
Izhar Ahmad, Anurag Jayswal, Babli Kumari, Characterizations of geodesic sub-\(b\)-\(s\)-convex functions on Riemannian manifolds, Journal of Nonlinear Sciences and Applications, 11 (2018), no. 2, 189--197
AMA Style
Ahmad Izhar, Jayswal Anurag, Kumari Babli, Characterizations of geodesic sub-\(b\)-\(s\)-convex functions on Riemannian manifolds. J. Nonlinear Sci. Appl. (2018); 11(2):189--197
Chicago/Turabian Style
Ahmad, Izhar, Jayswal, Anurag, Kumari, Babli. "Characterizations of geodesic sub-\(b\)-\(s\)-convex functions on Riemannian manifolds." Journal of Nonlinear Sciences and Applications, 11, no. 2 (2018): 189--197
Keywords
- Geodesic convex set
- geodesic sub-\(b\)-\(s\)-convex function
- optimality conditions
- Riemannian manifolds
MSC
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