Multivalued fixed point results in cone metric spaces

Journal of Inequalities and Applications, 2013

In this paper we extend the Banach contraction for multivalued mappings in a cone b-metric space without the assumption of normality on cones and generalize some attractive results in literature. MSC: 47H10; 54H25

The aim of this paper is to obtain extended variants of some common fixed point results in cone metric spaces in the case that the underlying cone is not normal. The first result concerns g-quasicontractions of D. Ilić and V. Rakočević [Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341 (2008), 876-882], and the second is concerned with Hardy-Rogers-type conditions and extends some recent results of M. Abbas, B. E. Rhoades and T. Nazir [Common fixed points for four maps in cone metric spaces, Appl. Math. Comput. 216 (2010), 80-86].

Various types of cones in topological vector spaces are discussed. In particular, the usage of (non)-solid and (non)-normal cones in fixed point results is presented. A recent result about normable cones is shown to be wrong. Finally, a Geraghty-type fixed point result in spaces with cones which are either solid or normal is obtained.

Journal of Ultra Scientist of Physical Sciences Section A

The main purpose of this paper is to prove some fixed point theorems and its applications in partial and generalized partial cone metric spaces. Our results are satisfying various contractive conditions on cone spaces. We also prove the uniqueness of such fixed points theorems.

Fixed Point Theory and Applications, 2009

We prove a result on points of coincidence and common fixed points for three self-mappings satisfying generalized contractive type conditions in cone metric spaces. We deduce some results on common fixed points for two self-mappings satisfying contractive type conditions in cone metric spaces. These results generalize some well-known recent results.

We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of normed-valued cone metric spaces. Examples are given to distinguish our results from the known ones.

In this paper, we study the existence of coincidence points and a unique common fixed point theorem for three self-mappings in cone metric spaces, where the cone is not necessarily normal. This result extends and improves recent related results in the literature.

The purpose of this paper is to translate a set of generalized contractive conditions for a couple of self-mappings to have a unique common fixed point in the language of cone metric spaces.

The Journal of Nonlinear Sciences and Applications, 2017

The aim of this paper is to introduce the notion of generalized Hausdorff distance function on G b -cone metric spaces and exploit it to study some fixed point results in the setting of G b -cone metric spaces without the assumption of normality. These results improve and generalize some important known results. Some illustrative examples are also furnished to highlight the realized improvements.

Rendiconti del Circolo Matematico di Palermo (1952 -), 2014

In this paper, we prove some common tripled fixed point and tripled coincidence point results for contractive conditions in a cone metric type space. Our results extend, unify and generalize well-known results in the literature, in particular the recent results of Aydi et al. (Fixed Point Theory Appl 2012:134, 2012. Some examples are also presented to validate our obtained results and new concepts.