Existence and Uniqueness of Zeros for Vector-Valued Functions with <i>K</i>-Adjustability Convexity and Their Applications

• Main Author: Wei-Shih Du
• Format: Article
• Language: English
• Published: MDPI AG 2019-09-01
• Series: Mathematics
• Subjects: <i>K</i>-convexity; strictly <i>K</i>-convexity; <i>K</i>-adjustability convexity; strictly <i>K</i>-adjustability convexity; nonlinear scalarization function; (<i>e</i>, <i>K</i>)-lower semicontinuous; zero for a vector-valued function; minimization problem; fixed point problem
• Online Access: https://www.mdpi.com/2227-7390/7/9/809
• ISSN: 2227-7390

In this paper, we introduce the new concepts of <i>K</i>-adjustability convexity and strictly <i>K</i>-adjustability convexity which respectively generalize and extend the concepts of <i>K</i>-convexity and strictly <i>K</i>-convexity. We establish some new existence and uniqueness theorems of zeros for vector-valued functions with <i>K</i>-adjustability convexity. As their applications, we obtain existence theorems for the minimization problem and fixed point problem which are original and quite different from the known results in the existing literature.