Generalized monotonicity and convexity of non-differentiable functions ✩

The relationships between (strict, strong) convexity of non-differentiable functions and (strict, strong) monotonicity of set-valued mappings, and (strict, strong, sharp) pseudo convexity of nondifferentiable functions and (strict, strong) pseudo monotonicity of set-valued mappings, as well as quasi convexity of non-differentiable functions and quasi monotonicity of set-valued mappings are studied in this paper. In addition, the relations between generalized convexity of non-differentiable functions and generalized co-coerciveness of set-valued mappings are also analyzed.  2003 Elsevier Science (USA). All rights reserved.