Fixed points of generalized $ \varphi $-concave-convex operators with mixed monotonicity and applications

Abstract

In this paper, we introduced a new concept of generalized $ \varphi $-concave-convex operator and proved the existence and uniqueness of fixed points of such operators with mixed monotonicity. As consequences, several new fixed point results about mixed monotone operators with some concavity and convexity were gained. In addition, the main results were applied to nonlinear integral equations on unbounded regions. The research findings generalized and developed recent relevant results in the literature.

Keywords

• generalized $ \varphi $-concave-convex operator
• mixed monotone operator
• fixed point