A Comparative Study of Ky Fan Hemicontinuity and Brezis Pseudomonotonicity of Mappings and Existence Results

Coercive and Noncoercive Mixed Generalized Complementarity Problems

“…Further, if Ψ is upper semicontinuous with respect to the first argument, then it is B-pseudomonotone. The converse of which is also true was asserted by Sadeqi and Paydar [29] in 2015. But later, in 2019, Steck [30] proved that the assertion of Sadeqi and Paydar was wrong by providing a counter example.…”

Brezis Pseudomonotonicity is Strictly Weaker than Ky–Fan Hemicontinuity

“…An interesting question that remains is where the argumentation from [15] is incorrect. The following is a particular error which is contained in that paper.…”

“…The following is a particular error which is contained in that paper. Remark 3.2 (An error in [15]). Proposition 3.5 of [15] is wrong.…”

“…This property implies Brezis pseudomonotonicity (a fact which follows directly from the corresponding definitions, see below), but the latter appears to be more refined and convenient when dealing with infinite-dimensional VIs. However, quite surprisingly, a 2015 publication by Sadeqi and Paydar [15] claims the equivalence of the two properties. The purpose of the present paper is to discuss this equivalence and provide a counterexample which shows that the two properties are in fact distinct.…”

“…An error in[15]). Proposition 3.5 of[15] is wrong. Choose K := E := ℓ 2 as the space of square-summable real sequences, F := Id E the identity mapping on E, and {u k } the sequence of unit vectors.…”