Some inequality techniques in handling fixed point problems on unbounded sets via homotopy methods

Abstract

Abstract As is well known, fixed point theorems and problems play important roles in differential equations, mathematical programming, control, and so on. In this paper, by providing some unboundedness conditions and by using some inequality techniques, we can give constructive proofs of the existence of fixed points on unbounded non-convex sets via homotopy methods.

Keywords

• Inequality techniques
• Constructive proofs
• Fixed point problems
• Homotopy methods