In this paper, we prove common fixed point theorems for a pair of weakly compatible maps under E.A .property. A major benefit of property (E.A.) is that it ensures convergence of desired sequences without completeness. At the end we rectify the main result of the paper, entitled “Common fixed points for weakly compatible maps, Proc. Indian Acad. Sci. (Math. Sci.) Vol. 111(2001), No. 2, pp 241-247.

For any space X, denote by dis(X) the smallest (infinite) cardinal κ such that κ many discrete subspaces are needed to cover X. It is easy to see that if X is any crowded (i.e. dense-in-itself) compactum then dis(X) m, where m denotes the additivity of the meager ideal on the reals. It is a natural, and apparently quite difficult, question whether in this inequality m could be replaced by c. He...

The notion of completeness on L-semi-uniform spaces is introduced in this paper. We have established that completeness is weakly hereditary and preserved under L-semi-uniform isomorphism. Finally, we have shown that in a totally bounded L-semi-uniform space, completeness is equivalent to compactness. 2010 AMS Classification: 54A40

The purpose of this paper is to obtain the common fixed point results for two pair of weakly compatible mapping by using common (CLR) property in partial metric space. Also we extend the very recent results which are presented in [17,  Muhammad Sarwar, Mian Bahadur Zada and Inci M. Erhan, Common Fixed Point Theorems of Integral type on Metric Spaces and application to system of functional equat...

We study the relation (and differences) between stability and Property (S) in simple stably finite framework. This leads us to characterize stable elements terms of their support, these concepts from different sides: hereditary subalgebras, projections multiplier algebra order properties Cuntz semigroup. use approaches show both that cancellation at infinity on semigroup just holds when its equ...

We explore properties of the set of d-units of a d-algebra. A property of interest in the study of d-units in d-algebras is the weak associative property. It is noted that many other d-algebras, especially BCK-algebras, are in fact weakly associative. The existence of d/BCK-algebras which are not weakly associative is demonstrated. Moreover, the notions of a d-integral domain and a left-injecti...

A Banach space X has property (S) if every weakly null sequence in BaX, the unit ball of X, has a subsequence which is C-dominated by the unit vector basis of c0 for some constant C < ∞. In [11] it was shown that if X has property (S), then the constant C can be chosen to be independent of the particular weakly null sequence in BaX. Here we generalize this result to the case of upper lp-estimates.

We introduce the notion of a hereditary property for rooted real trees and we also consider reduction of trees by a given hereditary property. Leaf-length erasure, also called trimming, is included as a special case of hereditary reduction. We only consider the metric structure of trees, and our framework is the space T of pointed isometry classes of locally compact rooted real trees equipped w...