In this paper we prove some fixed point theorems for Reich type contractions on cone rectangular metric spaces endowed with a graph without assuming the normality of cone. The results of this paper extends and generalize several known results from metric, rectangular metric, cone metric and cone rectangular metric spaces in cone rectangular metric spaces endowed with a graph. Some examples are ...

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function....

In this paper, we prove some fixed point theorems for ordered Reich type contraction in cone rectangular metric spaces without assuming the normality of cone. Our results generalize and extend some recent results in cone rectangular metric spaces, cone metric spaces and rectangular metric space. Some examples illustrating the results are included.

in this paper, using the fixed point theory in cone metric spaces, we prove the existence of a unique solution to a first-order ordinary differential equation with periodic boundary conditions in banach spaces admitting the existence of a lower solution.

A lot of authors have proved various common fixed-point results for pairs of self-mappings under strict contractive conditions in metric spaces. In the case of cone metric spaces, fixed point results are usually proved under assumption that the cone is normal. In the present paper we prove common fixed point results under strict contractive conditions in cone metric spaces using only the assump...

Since Huang and Zhang [1] introduced the concept of cone metric space, the study of common fixed points of mappings satisfying certain contractive conditions on cone metric spaces has been at the center of strong research activity, because it has not only important theoretical meaning but also wide applications. Recently, some authors obtained a number of meaningful consulting fixed point theor...

in this paper, several xed point theorems for t-contraction of two maps on cone metric spaces under normality condition are proved. obtained results extend and generalize well-known comparable results in the literature.

We introduce the notion of λ-spaces which is much weaker than cone metric spaces defined by Huang and X. Zhang 2007 . We establish some critical point theorems in the setting of λ-spaces and, in particular, in the setting of complete cone metric spaces. Our results generalize the critical point theorem proposed by Dancs et al. 1983 and the results given by Khanh and Quy 2010 to λ-spaces and con...

Abstract. In this paper, we introduce the concept of partial cone b-metric spaces as a generalization of partial metric, cone metric and b-metric spaces and establish some topological properties of partial cone b-metric spaces. Moreover, we also prove some common fixed point theorems for cyclic contractive mappings in such spaces. Our results generalize and extend the main results of Huang and ...

In this paper we introduce the concept of cone metric spaces with Banach algebras, replacing Banach spaces by Banach algebras as the underlying spaces of cone metric spaces. With this modification, we shall prove some fixed point theorems of generalized Lipschitz mappings with weaker conditions on generalized Lipschitz constants. An example shows that our main results concerning the fixed point...