New concepts of generalized ρ, θ -η invex functions for non-differentiable functions and generalized ρ, θ -η invariant monotone operators for set-valued mappings are introduced. The relationships between generalized ρ, θ -η invexity of functions and generalized ρ, θ -η invariant monotonicity of the corresponding Clarke’s subdifferentials are studied. Some of our results are extension and improv...

1 Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia 2 Department of Mathematical Sciences, Florida Institute of Techynology, Melbourne 32901, USA 3 Department of Mathematics, Aligarh Muslim University, Aligarh-202 002, India 4 Department of Mathematics, Faculty of Applied Sciences, Integral University, Lucknow 226026, India 5 D...

In this paper, several kinds of invariant monotone maps and generalized invariant monotone maps are introduced. Some examples are given which show that invariant monotonicity and generalized invariant monotonicity are proper generalizations of monotonicity and generalized monotonicity. Relationships between generalized invariant monotonicity and generalized invexity are established. Our results...

In this paper, we introduce a new class of generalized convex function, namely, α-pseudounivex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinem...