Metrical common fixed point theorems without completeness and closedness
نویسندگان
چکیده
* Correspondence: [email protected] Department of Mathematics and Humanities, S.V. National Institute of Technology, Surat, Gujarat, India Full list of author information is available at the end of the article Abstract In this article, we point out that some recent results proved in Babu and Alemayehu are corollaries of the main result of an article due to Ali and Imdad. However, combining the notions of R-weakly commuting property of type (Ag) (due to Pathak et al. together with sequential continuity of type (Ag) (to be introduced in this note) (also alternately R-weakly commuting property of type (Af) (due to Pathak et al.) together with sequential continuity of type (Af) (to be introduced in this note)) these results are improved which are possibly new results in the literature of metric fixed point theory. Mathematics Subject Classification (2000): 47H06; 47H10.
منابع مشابه
Suzuki-type fixed point theorems for generalized contractive mappings that characterize metric completeness
Inspired by the work of Suzuki in [T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2008), 1861--1869], we prove a fixed point theorem for contractive mappings that generalizes a theorem of Geraghty in [M.A. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), 604--608]an...
متن کاملCoincidence and Fixed Points in G - Metric Spaces ( Communicated by Daniel Pellegrino )
The intent of this paper is to extend the notions of occasionally weakly compatible mappings, subcompatibility and subsequential continuity in framework of generalized metric spaces and prove some common fixed point theorems. We give some examples which demonstrate the validity of the hypotheses and degree of generality of our results. Our results are independent of the continuity requirement o...
متن کاملCommon Fixed Point Theorems on Fuzzy Metric Spaces Using Implicit Relation
Received: 27 March 2012; Accepted: 25 July 2012. Published online: XX July. 2012 Abstract: In this paper, we prove a common fixed point theorem for occasionally weakly compatible mappings on fuzzy metric space satisfying an implicit relation. Our result never requires the completeness (or closedness) of the whole space (or subspaces), containment of ranges amongst involved mappings and continui...
متن کامل(Non)-completeness of R–buildings and fixed point theorems
We prove two generalizations of results appearing in [4] involving metrical completeness and R–buildings. Firstly, we give a generalization of the Bruhat–Tits fixed point theorem also valid for non-complete R–buildings, but with the added condition that the group is finitely generated. Secondly, we generalize a criterion which reduces the problem of completeness to the wall trees of the R–build...
متن کاملFixed point theorems for generalized quasi-contractions in cone $b$-metric spaces over Banach algebras without the assumption of normality with applications
In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the assumption of normality we establish common fixed point theorems for the generalized quasi-contractions with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$ in the set...
متن کامل