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<p>This paper builds on the work of Bessem Samet by introducing new results in the context of (<i>v</i>,&#xa0;<i>w</i>)-convex functions, both in general and for differentiable cases. The study extends the definition of (<i>v</i>,&#xa0;<i>w</i>)-convex functions from Euclidean space to Riemannian manifolds, leading to the concept of geodesic (<i>v</i>,&#xa0;<i>w</i>)-convex functions. Several theorems are proven, including results that show the preservation of (<i>v</i>,&#xa0;<i>w</i>)-convexity under summation and positive scalar multiplication of functions. Additionally, the paper presents novel findings on (<i>v</i>,&#xa0;<i>w</i>)-convexity in Riemannian manifolds, providing a theoretical foundation for future exploration. The developed theorems are also applied to nonlinear programming, offering a method to find optimal solutions for differentiable functions within this framework. This research contributes to both the theory of convexity and its applications in optimization problems on Riemannian manifolds.</p>

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Some properties and applications of (v, w)-convex functions

  • 期刊论文

  • 发表日期：

    2025年5月3日

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  • Ehtesham Akhter,
  • Musavvir Ali

摘要

This paper builds on the work of Bessem Samet by introducing new results in the context of (v, w)-convex functions, both in general and for differentiable cases. The study extends the definition of (v, w)-convex functions from Euclidean space to Riemannian manifolds, leading to the concept of geodesic (v, w)-convex functions. Several theorems are proven, including results that show the preservation of (v, w)-convexity under summation and positive scalar multiplication of functions. Additionally, the paper presents novel findings on (v, w)-convexity in Riemannian manifolds, providing a theoretical foundation for future exploration. The developed theorems are also applied to nonlinear programming, offering a method to find optimal solutions for differentiable functions within this framework. This research contributes to both the theory of convexity and its applications in optimization problems on Riemannian manifolds.