Few Common Fixed Point Results For Weakly Commuting Mappings (original) (raw)
FIXED POINT AND WEAK COMMUTING MAPPING
IJRET, 2012
In this paper we prove some new fixed point theorems for weak commuting mapping on complete metric space. Our results generalize several corresponding relations in metric space of weak commuting mapping
On common fixed points of weakly commuting mappings and set-valued mappings
International Journal of Mathematics and Mathematical Sciences, 1986
Our main theorem establishes the uniqueness of the common fixed point of tw set-valued mappings and of two single-valued mappings defined on a complete metric space, under a contractive condition and a weak commutativity concept. This improves a theorem of the second author. K'Y WORDS AND PHRASES. Common fixed point, set-valued mappin., weak eomutativity. 1080 AMS SUBJECT CLASSIFICATION CODES. 54H25, 47H10. Let (X,d) be a complete metric space and let B(X) be the set of all nonempty, bounded subsets of X As in [I], let (A,B) be the function defined by (A,B) sup {d(a,b) a A, b B} for all A, B in B(X). If A consists of a single point a we write 6(A,B) (a,B) and if B also consists of a single point b we write (A,B) d(a,b) It follows immediately from the definition that
FIXED POINT THEOREM FOR COMMUTING MAPPING
It can be observed that completeness of a metric space is not enough to ensure the existence of fixed point for contractive mappings. So, fixed point theorems for such mappings require further restriction on the space or extra conditions have to be imposed on mappings or some restrictions imposed on its range. Edelstein had shown that compactness of the metric space (X,d) guarantees a unique fixed point for a contractive mapping on X. In this paper,the commutative maps are used as a tool for generalizing some of the results.
Some Fixed Point Results forTAC-Type Contractive Mappings
Journal of Function Spaces, 2016
We prove some fixed point results for new type of contractive mappings using the notion of cyclic admissible mappings in the framework of metric spaces. Our results extend, generalize, and improve some well-known results from literature. Some examples are given to support our main results.
A new condition for the existence of a common fixed point for two commutatingself-mappings
In this paper, we prove the existence of a common fixed point for two commuta-tive mappings satisfying and generalizing contractive conditions. We provide a newcondition on one of them which leads us to Juncgk’s theorem. Moreover, we estab-lish the associated Banach theorem. Our results generalize some known results in theliterature. 2010 Mathematics Subject Classi cation: Primary 54H25, secondary 47H10.
Mathematical Sciences, 2013
In this paper, we prove some common fixed point theorems for weakly compatible mappings in metric spaces satisfying generalized (ψ, ϕ)-contractive conditions under the common limit range property. We present a fixed point theorem for four finite families of self-mappings which can be utilized to derive common fixed point theorems involving any number of finite mappings. Our results improve and extend the corresponding results of Radenović et al. (Bull. Iranian Math. Soc. 38(3):625-645, 2012). We also furnish some illustrative examples to support our main results. The concept of weak contraction was introduced by Alber and Guerre-Delabriere [7] in 1997, wherein the authors introduced the following notion for mappings defined on a Hilbert space X. Consider the following set of real functions = { ϕ : [ 0, +∞) →[ 0, +∞) : ϕ is lower semi-continuous and ϕ −1 ({0}) = {0} }.