We generalize some results of Borwein, Burke, Lewis, and Wang to mappings with values in metric (resp. ordered normed linear) spaces. We define two classes of monotone mappings between an ordered linear space and a metric space (resp. ordered linear space): K-monotone dominated and coneto-cone monotone mappings. K-monotone dominated mappings naturally generalize mappings with finite variation (...

[Perov, A. I., On Cauchy problem for a system of ordinary diferential equations, (in Russian), Priblizhen. Metody Reshen. Difer. Uravn., 2 (1964), 115-134] used the concept of vector valued metric space and obtained a Banach type fixed point theorem on such a complete generalized metric space. In this article we study fixed point results for the new extensions of Banach’s contraction principle ...

Let P be a subset of a Banach space E and P is normal and regular cone on E, we prove the existence of the fixed point for multivalued maps in cone metric spaces and these theorems generalize the Bose and Mukerjee results and the results of varies authors.

The aim of this paper is to prove a common fixed point theorem for two pairs of self mappings in a cone metric space without assuming the normality of cone. Here we consider one pair of compatible mappings of type (R) and another pair of weakly compatible. Our results extend and modify the result of [11] and generalise many other results in the literature. −−−−−−−−−−−−−−−−−−−−−−−−−−−−

Let P be a sub set of Banach space E and P is normal and regular cone on E; we generalize and obtain some sufficient conditions for the existence of common fixed point of multivalued mappings satisfying contractive type conditions in cone metric spaces. Our results unify, generalize and complement the comparable results from the current literature.

In this paper a completion theorem for cone metric spaces and a completion theorem for cone normed spaces are proved. The completion spaces are defined by means of an equivalence relation obtained by convergence via the scalar norm of the Banach space E.

the sequential $p$-convergence in a fuzzy metric space, in the sense of george and veeramani, was introduced by d. mihet as a weaker concept than convergence. here we introduce a stronger concept called $s$-convergence, and we characterize those fuzzy metric spaces in which convergent sequences are $s$-convergent. in such a case $m$ is called an $s$-fuzzy metric. if $(n_m,ast)$ is a fuzzy metri...

The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for three self mappings in $b$-metric spaces. Next, we obtain cone $b$-metric version of these results by using a scalarization function. Our results extend and generalize several well known comparable results in the existing literature.

In 2007, Huang and Zhang in 1 introduced cone metric space by substituting an ordered Banach space for the real numbers and proved some fixed point theorems in this space. Many authors study this subject and many fixed point theorems are proved; see 2–5 . In this paper, the concept of integral in this space is introduced and a fixed point theorem is proved. In order to do this, we recall some d...

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 ...