In classical fixed point and coincidence theory the notion of Nielsen numbers has proved to be extremely fruitful. Here we extend it to pairs (f1, f2) of maps between manifolds of arbitrary dimensions. This leads to estimates of the minimum numbers MCC(f1, f2) (and MC(f1, f2), resp.) of pathcomponents (and of points, resp.) in the coincidence sets of those pairs of maps which are homotopic to (...

The purpose of this paper is to establish coincidence point and common fixed point results for four maps satisfying generalized weak contractions in cone metric spaces. Also, an example is given to illustrate our results.

Abstract. In this paper, we prove results on n-tupled coincidence as well as n-tupled fixed point in partially ordered complete metric spaces for a pair of weakly contractive compatible mappings whenever n is even, wherein control functions are also employed. Our main theorem improves the corresponding results of Choudhury et al. (Ann. Univ. Ferrara 57: 1-16, 2011). We illustrate our main resul...

Abstract. In this paper, we prove some fixed point results for T -contraction mappings in partially ordered b-metric spaces that generalize the main results of [H. Huang, S. Radenović, J. Vujaković, On some recent coincidence and immediate consequences in partially ordered b-metric spaces, Fixed Point Theory Appl., 2015, Paper No. 63]. As an application, we discuss the existence for a solution ...

It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...

The notion of coupled fixed point was initiated by Gnana Bhaskar and Lakshmikantham 1 in 2006. In this paper, they proved some fixed point theorems under a set of conditions and utilized their theorems to prove the existence of solutions to some ordinary differential equations. Recently, Berinde and Borcut 2 introduced the notion of tripled fixed point and extended the results of Gnana Bhaskar ...

The notion of coupled fixed point is introduced by Gnana-Bhaskar and Lakshmikantham. Very recently, the concept of tripled fixed point was introduced by Berinde and Borcut. In this manuscript, a quadruple fixed point is considered and some new related fixed point theorems are obtained. We also give some examples to illustrate our results. © 2012 Elsevier Ltd. All rights reserved.

The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings having a mixed g-monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend sever...