Special type convex functions on Riemannian manifolds with application

Ehtesham Akhter; Musavvir Ali; Mohd Bilal; Ehtesham Akhter; Musavvir Ali; Mohd Bilal

doi:10.3934/math.2023770

AIMS Mathematics

2023, Volume 8, Issue 7: 15081-15091. doi: 10.3934/math.2023770

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Special type convex functions on Riemannian manifolds with application

1.
Department of Mathematics, Aligarh Muslim University, Aligarh-202002, India
2.
Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al Qura University, Makkah, 21955, KSA

Received: 28 January 2023 Revised: 24 March 2023 Accepted: 06 April 2023 Published: 23 April 2023
MSC : 52A20, 52A41, 53C20, 53C22

In this manuscript, we define a special type convex function on Euclidean space and explore it on the Riemannian manifold. We also detail the fundamental properties of special type convex functions and some examples that illustrate the idea. Moreover, to demonstrate the application to the problems of optimization, these special type convex functions are used.
- special type convexity,
- special subgradient,
- inequality,
- optimization,
- manifolds
Citation: Ehtesham Akhter, Musavvir Ali, Mohd Bilal. Special type convex functions on Riemannian manifolds with application[J]. AIMS Mathematics, 2023, 8(7): 15081-15091. doi: 10.3934/math.2023770

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Abstract

In this manuscript, we define a special type convex function on Euclidean space and explore it on the Riemannian manifold. We also detail the fundamental properties of special type convex functions and some examples that illustrate the idea. Moreover, to demonstrate the application to the problems of optimization, these special type convex functions are used.

References

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