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A Study of Geodesic ( E , F )-Preinvex Functions on Riemannian Manifolds

Author

Listed:
  • Ehtesham Akhter

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

  • Mohd Bilal

    (Department of Mathematical Sciences, Faculty of Applied Sciences, Umm Al-Qura University, Makkah 21955, Saudi Arabia)

  • Musavvir Ali

    (Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India)

Abstract

In this manuscript, we define the ( E , F ) -invex set, ( E , F ) -invex functions, and ( E , F ) -preinvex functions on Euclidean space, i.e., simply vector space. We extend these concepts on the Riemannian manifold. We also detail the fundamental properties of ( E , F ) -preinvex functions and provide some examples that illustrate the concepts well. We have established a relation between ( E , F ) -invex and ( E , F ) -preinvex functions on Riemannian manifolds. We introduce the conditions A and define the ( E , F ) -proximal sub-gradient. ( E , F ) -preinvex functions are also used to demonstrate their applicability in optimization problems. In the last, we establish the points of extrema of a non-smooth ( E , F ) -preinvex functions on ( E , F ) -invex subset of the Riemannian manifolds by using the ( E , F ) -proximal sub-gradient.

Suggested Citation

  • Ehtesham Akhter & Mohd Bilal & Musavvir Ali, 2025. "A Study of Geodesic ( E , F )-Preinvex Functions on Riemannian Manifolds," Mathematics, MDPI, vol. 13(6), pages 1-9, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:896-:d:1607621
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