arXiv subjects
Publications and source records attributed to Allahkaram Shafie.
In this work, some counterexamples are given to refute some results reported in the paper by Guo and Li [8] (J Optim Theory Appl 162,(2014), 821-844). We correct the faulty in some of their theorems and we present alternative proofs. Moreover, we extend the definition of approximately pseudo-dissipative in the setting of metrizable topological vector spaces.
In this short paper, Kuratowski problem will be investigated in vector space. The highest number of distinct sets that can be generated from one convex set in linear space by repeatedly applying algebraic closure and complement in any order is 8. Keywords: Kuratowski problem, algebraic interior, algebraic closure
In this paper, we prove the existence of a solution to the Stampachia variational inequality under weakened assumptions on the given operator. As a consequence, we provide some sufficient conditions that under them the generalized equation $0\in T(x)$ has a solution. Furthermore, by using generalized results of continuity and monotonicity, we extend the related existence results and we answer an open problem proposed by Kassay and Miholka (J Optim Theory Appl 159 (2013) 721-740).