Hasan Abu-Donia

Zagazig University · Department of Mathematics

This study presents fundamental theorems, lemmas, and mapping definitions. There are three types of mappings: binary operators, compatible mappings, and sequentially continuous mappings. The symbols used to represent fuzzy metric spaces are intuitive. Icons were also used to prescribe a shared, linked fixed point in intuitionistic fuzzy metric spac...

In order to meet the ψ–contractive criteria, two sets of compatible and sequentially continuous mappings in the modified intuitionistic fuzzy metric space are shown to have a shared triple fixed point. The binary operator, intuitionistic fuzzy metric space, modified intuitionistic fuzzy metric space, and compatible mapping are only a few of the mor...

This study establishes a common coupled fixed point for two pairs of compatible and sequentially continuous mappings in the intuitionistic fuzzy metric space that satisfy the ϕ–contractive conditions. Many basic definitions and theorems have been used from some recent scientific papers about the binary operator, t-norm, t-conorm, intuitionistic fuz...

In this paper, we studied the separability of the non-linear Schrodinger operator of the form S u x = − Δ u x + V x , u u x , where Δ u x = ∑ i = 1 n ∂ 2 u x ∂ x i 2 , $Su\left(x\right)=-{\Delta}u\left(x\right)+V\left(x,u\right)u\left(x\right),\,\text{where}\,{\Delta}u\left(x\right)={\sum }_{i=1}^{n}\frac{{\partial }^{2}u\left(x\right)}{\partial {x...

This research paper investigates and proves some theorems of the fixed point for self–mapping [T:X→X] under (ϕ,ψ)–contractive mappings and (ϕ,φ)–contractive mappings in Menger probabilistic 2–metric space. These theorems are used as an essential tool to convert the probabilistic metric to 2–metric space and are employed to prove the uniqueness and...

In this paper, we generalize the two types of Yao’s lower and upper approximations, using finite number of reflexive relations. Moreover, we give a comparison between these types and study some properties.

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 neighbo...

In this paper, we introduce a new type of closed sets in bitopological space (X, τ1, τ2), used it to construct new types of normality, and introduce new forms of continuous function between bitopological spaces. Finally, we proved that the our new normality properties are preserved under some types of continuous functions between bitopological spac...

Rough set theory was introduced by Pawlak in 1982 to handle imprecision, vagueness, and uncertainty in data analysis. Our aim is to generalize rough set theory by introducing concepts of -lower and -upper approximations which depends on the concept of -sets. Also, we study some of their basic properties.

The original rough set model was developed by Pawlak, which is mainly concerned with the approximation of objects using an equivalence relation on the universe of his approximation space. This paper extends Pawlak’s rough set theory to a topological model where the set approximations are defined using the topological notion δβ-open sets. A number o...

The purpose of this work is to study common fixed point theorems for six mappings and sequences of mappings satisfying a contractive condition of integral type. Our results improve, extend and generalize corresponding results given by many authors.

Rough set theory is an important technique in knowledge discovery in databases. In covering based rough sets, many types of rough set models are established in recent years. This paper presents new types of rough set approximations using multi knowledge base, that is, family of finite number of (reflexive, tolerance, dominance, equivalence) relatio...

The aim of this paper is to introduce three approaches to near sets by using a multi-valued system. Some fundamental properties and characterizations are given. We obtain a comparison among these types of approximations. The contribution of this paper is to form basis for the discovery of perceptual objects that are descriptively near each other.

Functions are a means to link or transport from a world to another world may be similarly or completely different from the other world. In this paper we addressed the issue of rough functions and the possibility of transfer it from the real line to the topological abstract view that can be applied to intelligent information systems. The rough funct...

The aim of this paper is to introduce two approaches to near sets by using a special neighbourhood. Some fundamental properties and characterizations are given. We obtain a comparison between these new set approximations as well as set approximations introduced by Peters �2011, 2009, 2007, 2006�.

The purpose of this paper is to introduce some types of compatibility of maps. We prove some common fixed-point theorems for mappings satisfying some conditions on intuitionistic fuzzy metric spaces, which were defined by J. H. Park [Chaos Solitons Fractals 22, No. 5, 1039–1046 (2004; Zbl 1060.54010)].

In this paper we generalize the concept of simple expansion due to Levine (1964) to the fuzzy setting. Also, we introduce new classes of fuzzy sets, namely fuzzy η-preopen sets, fuzzy weakly η-open sets and fuzzy weakly η-preopen sets. This families not only depend on the fuzzy topology τ but also on it simple expansion and we study their fundament...

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The purpose of this paper is to study common fixed point theorems for set-valued and single-valued mappings in fuzzy metric, fuzzy 2-metric and fuzzy 3-metric spaces. We extend new definitions in fuzzy metric, fuzzy 2-metric and fuzzy 3-metric spaces. Also, we extend results of B. Fisher [Math. Semin. Notes, Kobe Univ. 7, 81–84 (1979; Zbl 0415.5403...

The purpose of this paper is to establish common fixed point theorems for set-valued mappings between 2-metric spaces. Generalizations of some definitions in 2-metric spaces and theorems by M. A. Ahmed [Rocky Mt. J. Math. 33, No. 4, 1189–1203 (2003; Zbl 1065.47051)], generalized of B. Fisher [Kyungpook Math. J. 25, 35–42 (1985; Zbl 0582.54032)] in...

We prove common fixed point theorems for four mappings in fuzzy metric, fuzzy 2-metric and fuzzy 3-metric spaces.

In this paper, we discuss three types of lower and upper approximations of any set with respect to any relation based on right neighborhood. We generalize these three types of approximations into two ways by using a finite number of any binary relations. The first way based on the intersection of the right neighborhoods for a family of binary relat...

Some common fixed point theorems for multi-valued mappings under ϕ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for ϕ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194–204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191–207] and Helipern [Hilpern S. F...

The purpose of this paper is to study a common fixed point theorems on 2-metric spaces. Generalizations some definitions on 2-metric spaces and Fisher theorems [2] on 2-metric spaces.

The aim of this paper is to introduce a new method for approximation of sets by using a finite numbers of information systems. Some fundamental properties and characterizations are given and we obtain the comparison between this type of approximation and Pawlak approximation.

The purpose of the present work is to construct a new method for approximation of sets using two information systems simultaneously. Some properties and characterizations are given and a comparison with the previous sorts of approximation is obtained.

In this paper we introduce some classes of sets in a bitopological space (X, τ1, τ2). We show that some of these classes are infra topologies and some are supra topologies. Also, we use these classes to introduce new bitopological properties and new types of continuous functions between bitopological spaces. We prove that some of the introduced bit...

In this paper we give an approach for constructing classes of near open and near closed sets which have unusual implication relations. These new classes of subsets are based on the alternative effect of closure and interior operators with respect to two topologies. Also these classes of subsets are applied for constructing several classes of near c...