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2021•Khayyam journal of mathematicsOpen access

Some properties of geodesic $(alpha,E)$-preinvex functions on Riemannian manifolds

Absos Ali Shaikh, Chandan Kumar Mondal, Ravi P. Agarwal

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Geodesic, Riemannian manifold, Mathematics, Geodesic map, Manifold (fluid mechanics), Pure mathematics, Function (biology), Alpha (finance)

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