arXiv subjects
Publications and source records attributed to Issa Mohamadi.
We establish the first common fixed point theorem for commutative set-valued mappings. This may help to generalize common fixed point theorems in single-valued setting to those in set-valued. We also prove the existence of a fixed point in a continuously expanding set under a none convex upper semicontinuous set-valued mapping; as a result we answer positivly to a question of Lau and Yao.
The expansion of the universe has been accepted by scientists for more than a century. However, since the 1990s, observations have suggested that the universe is expanding at an accelerating rate. Although the source of this acceleration is still unknown, cosmologists call it dark energy; a type mysterious energy which exerts a negative pressure on the universe. In this paper, applying different approach from those of classical mathematical physics based mainly on functional analysis, we propose an answer to this question. In fact, we first establish a theorem for multivalued mappings; and as result we apply this theorem to show the existence of a remnant field of high energy in a continuously expanding system of energy. The results may also be applied to the early universe to show the existence of a possible source for dark energy. The answer is partially confirmed by a paper published in Nature Asronomy.