Fixed Points of Generalized ϕ Concave‐(−ψ) Convex Operators With Mixed Monotonicity and Applications to Nonlinear Integral Equations

ABSTRACT In this paper, the concept of generalized concave‐ convex operator is introduced, and some fixed point theorems of this class of operators with mixed monotonicity are set up. As a consequence, a number of new fixed point results on mixed monotone operators with certain concavity and convexity are obtained. In addition, the main theoretical results are applied to nonlinear Hammerstein integral equations. Our results and application examples extend and improve related previous work.