The fixed point theorems of 1-set-contractive operators in Banach space

Abstract

Abstract In this paper, we obtain some new fixed point theorems and existence theorems of solutions for the equation Ax = μx using properties of strictly convex (concave) function and theories of topological degree. Our results and methods are different from the corresponding ones announced by many others. MSC: 47H09, 47H10

Keywords

• 1-Set-contractive operator
• Topological degree
• Convex function
• Concave function
• Fixed point theorems