Let $R$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $R$ and $f(X)=a_0+a_1X+cdots+a_nX^n$ be a nonzero skew polynomial in $R[X;alpha]$. It is proved that if there exists a nonzero skew polynomial $g(X)=b_0+b_1X+cdots+b_mX^m$ in $R[X;alpha]$ such that $g(X)f(X)=c$ is a constant in $R$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $R$ such tha...

Using Calegari's result on the Fontaine-Mazur conjecture, we study irreducibility of pure, regular, rank 3 weakly compatible systems self-dual l-adic representations. As a consequence, prove that Tate conjecture holds for family elliptic surfaces defined over Q with geometric genus bigger than 1.

In this paper, we prove a general common fixed point theorem for two pairs of weakly compatible self-mappings of a metric space satisfying a weak Meir-Keeler type contractive condition by using a class of implicit relations. In particular, our result generalizes and improves a result of K. Jha, R.P. Pant, S.L. Singh, by removing the assumption of continuity, relaxing compatibility to weakly com...

* Correspondence: poom. [email protected] Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (Kmutt), Bangkok 10140, Thailand Abstract In this article, we introduce two new different classes of noncommuting selfmaps. The first class is more general than JH-operator class of Hussain et al. (Common fixed points for JH-operators and occasionally weakly bi...

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.

Abstract We prove the existence and uniqueness of fixed points some generalized contractible operators defined on modular G -metric spaces also -continuity such operators. Furthermore, we that weakly compatible contractive in have a unique point. Our results extend, generalize, complement include several known as special cases.

We endow the set of real numbers with a family of fuzzy quasi-metrics, in the sense of George and Veeramani, which are compatible with the Sorgenfrey topology. Although these fuzzy quasi-metrics are not deduced explicitly from a quasi-metric, they possess interesting properties related to completeness. For instance, we prove that they are balanced and complete in the sense of Doitchinov and tha...

In this paper, we prove a common fixed point theorem for a pair of weakly compatible mappings. The result is applied to prove the existence of solution of system of nonlinear integral equations. Our theorems extend and improve several known results. c © 2007 Elsevier Ltd. All rights reserved.

Recommended by Wolfgang Kuehnel We introduce a new generalized contractive condition for four mappings in the framework of metric space. We give some common fixed point results for these mappings and we deduce a fixed point result for weakly compatible mappings satisfying a contractive condition of integral type.

In this paper, we prove some common fixed point theorems for two pairs of weakly compatible selfmaps satisfying a new ψ-contractive condition in the framework of a partial metric space. We also provide illustrative examples in support of our new results. The results obtained in this paper differ from the recent relative results in literature. c ©2016 All rights reserved.