Duran Turkoglu

Common fixed point theorems in intuitionistic fuzzy metric spaces

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck’s common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant’s theorem ([21]).

Fixed Points of Weakly Compatible Maps Satisfying a General Contractive Condition of Integral Type

We prove a fixed point theorem for weakly compatible maps satisfying a general contractive condition of integral type.

SOME FIXED POINT THEOREMS ON FUZZY METRIC SPACES WITH IMPLICIT RELATIONS

In this paper, we give some fixed point theorems on fuzzy metric spaces with an implicit relation. Our results extend and generalize some fixed point theorems on complete fuzzy metric spaces by using a new technique.

ON COMPATIBLE MAPPINGS OF TYPE (I) AND (II) IN INTUITIONISTIC FUZZY METRIC SPACES

In this paper, we give some new definitions of compatible mappings in intuitionistic fuzzy metric spaces and we prove a common fixed point theorem for four mappings under the condition of compatible mappings of type (I) and of type (II) in complete intuitionistic fuzzy metric spaces.

A note on common fixed points for ( ψ , α , β ) -weakly contractive mappings in generalized metric spaces

Very recently, Isik and Turkoglu (Fixed Point Theory Appl. 2013:131, 2013) proved a common fixed point theorem in a rectangular metric space by using three auxiliary distance functions. In this paper, we note that this result can be derived from the recent paper of Lakzian and Samet (Appl. Math. Lett. 25:902-906, 2012).MSC:47H10, 54H25.

Best approximations theorem for a couple in cone Banach space.

The notion of coupled fixed point is introduced by Bhaskar and Lakshmikantham, (2006). In this manuscript, some result of Mitrović, (2010) extended to the class of cone Banach spaces.

Compatible Maps and Compatible Maps of Types (α) and (β) in Intuitionistic Fuzzy Metric Spaces

In this paper, we first formulate the definition of compatible maps and compatible maps of types (a) and (/3) in intuitionistic fuzzy metric spaces and give some relations between the concepts of compatible maps and compatible maps of types (a) and 03). Introduction In 1965, the concept of fuzzy sets was introduced by Zadeh [25]. Since then many authors have expansively developed the theory of fuzzy sets and applications. Especially, Deng [5], Erceg [7], Kaleva and Seikkala [15], Kramosil and Michalek [18] have introduced the concepts of fuzzy metric space in different ways. George and Veeramani [8, 9] modified the concept of fuzzy metric spaces introduced by Kramosil and Michalek and defined the Hausdorff topology of fuzzy metric spaces. They showed also that every metric induces a fuzzy metric. Grabiec [10] extended the well known fixed point theorem of Banach and Edelstein [6] to fuzzy metric spaces in the sense of Kramosil and Michalek. Grabiec and Kramosil and Michalek, Mishra et al. [20] and many authors [11-14, 20, 22, 24] obtained common fixed point theorems for compatible maps and asymptotically commuting maps on fuzzy metric spaces, which generalize, extend and fuzzify several fixed point theorems for contractivetype maps on metric spaces and other spaces. Cho et al. [3] first formulate the definition of compatible maps of type (/3) in fuzzy metric spaces and give some relations between the concepts of compatible maps and compatible 1991 Mathematics Subject Classification: 54H25, 47H10.

Fixed point of multivalued mapping in uniform spaces

In this paper we prove some new fixed point theorems for multivalued mappings on orbitally complete uniform spaces.

Some Fixed-Point Theorems for Multivalued Monotone Mappings in Ordered Uniform Space

We use the order relation on uniform spaces defined by Altun and Imdad (2009) to prove some new fixed-point and coupled fixed-point theorems for multivalued monotone mappings in ordered uniform spaces.

Common fixed points for (ψ, α, β)-weakly contractive mappings in generalized metric spaces

We establish some common fixed point theorems for mappings satisfying a (ψ,α,β)-weakly contractive condition in generalized metric spaces. Presented theorems extend and generalize many existing results in the literature.MSC: Primary 54H25; secondary 47H10.