Common Fixed Point Theorems For Finite Number Of Mappings Without Continuity And Compatibility In Menger Spaces
نویسنده
چکیده
Introduction Sessa [9] generalized the notion of commuting maps given by Jungck [2] and introduced weakly commuting mappings. Further, Jungck [3] introduced more generalized commutativity called compatibility. In 1998, Jungck and Rhoades [4] introduced the notion of weakly compatible maps and showed that compatible maps are weakly compatible but converse need not true. Menger [5] introduced the notion of probabilistic metric space, which is generalization of metric space and study of these spaces was expanded rapidly with pioneering work of Schewizer and Sklar [7], [8]. The existence of fixed points for compatible mappings on probabilistic metric space is shown by Mishra [6]Most of the fixed point theorems in Menger spaces deal with conditions of continuity and compatibility or compatibility of type (α) or compatible of type (β). There are maps which are not continuous but have fixed points. Also weakly compatible maps defined by Jungck and Rhoades [4] are weaker than that of compatibility. To prove existence of common fixed point for finite number of mappings some commutativity conditions are required.
منابع مشابه
Common fixed point theorems for occasionally weakly compatible mappings in Menger spaces and applications
In 2008, Al-Thaga and Shahzad [Generalized I-nonexpansive self-maps and invariant approximations, Acta Math. Sinica 24(5) (2008), 867{876]introduced the notion of occasionally weakly compatible mappings (shortly owcmaps) which is more general than all the commutativity concepts. In the presentpaper, we prove common xed point theorems for families of owc maps in Mengerspaces. As applications to ...
متن کاملSome fixed point theorems for weakly subsequentially continuous and compatible of type (E) mappings with an application
In this paper, we will establish some xed point results for two pairs of self mappings satisfying generalized contractive condition by using a new concept as weak subsequential continuity with compatibility of type (E) in metric spaces, as an application the existence of unique common solution for a system of functional equations arising in system programming is proved.
متن کاملA new approximation method for common fixed points of a finite family of nonexpansive non-self mappings in Banach spaces
In this paper, we introduce a new iterative scheme to approximate a common fixed point for a finite family of nonexpansive non-self mappings. Strong convergence theorems of the proposed iteration in Banach spaces.
متن کاملCommon Fixed Point Theorems for Sequences of Mappings under General Contractive Condition of Integral Type in Fuzzy Metric Spaces
The purpose of this paper is to study common fixed point theorems for six (four single-valued and two set-valued) mappings in fuzzy metric space using general contractive condition of integral type, without assuming compatibility and continuity of any mapping on non complete metric spaces. To prove the theorems, we use a non compatible condition, that is, weak commutativity of type (Kh)in fuzzy...
متن کامل