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The concept of a 2-metric space is a natural generalization of a metric space. It has been investigated initially by Gähler [4]. Iseki [5] studied the fixed point theorems in 2-metric spaces. Sessa [17] defined weak commutativity and proved common fixed point theorem for weakly commuting maps. In [7] Jungck introduced more generalized commuting mappings,… (More)

The purpose of this paper is to study common fixed point theorems for a setvalued and single-valued mappings in a metric spaces. Generalizations and extensions of known results are thereby obtained. In particular, the theorems by Ahmed [1], Ahmed [2], Rashwan and Ahmed [13], Skof [16], Rhoades, Tiwary and Singh [14] and Kiventidis [10] are improved.

- Emad A. Marei, Mohamed E. Abd El-Monsef, Hassan M. Abu-Donia
- Fundam. Inform.
- 2015

Most real life situations need some sort of approximation to fit mathematical models. The beauty of using topology in approximation is achieved via obtaining approximation for qualitative subsets without coding or using assumption. The aim of this paper is to introduce different approaches to near sets by using general relations and special neighbourhoods.… (More)

The concept of a preopen set in a topological space was introduced by H. H. Corson and E. Michael in 1964 [3]. A subset A of a topological space (X, τ) is called preopen or locally dense or nearly open if A ⊆ Int(Cl(A)). A set A is called preclosed if its complement is preopen or equivalently if Cl(Int(A)) ⊆ A. The term, preopen, was used for the first time… (More)

The concept of a pre-open set in a topological space was introduced by H. H. Corson and E. Michael in 1964 [3]. A subset A of a topological space (X, τ) is called pre-open or locally dense or nearly open if A ⊆ Int(Cl(A)). A set A is called pre-closed if its complement is preopen or equivalently if Cl(Int(A)) ⊆ A. The term, pre-open, was used for the first… (More)

- Mohamed E. Abd El-Monsef, Hassan M. Abu-Donia, Emad A. Marei
- Trans. Rough Sets
- 2012

The aim of this paper is to introduce three approaches to near sets by using a multivalued system. Some fundamental properties and characterizations are given. We obtain a comparison among these types of approximations.

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