Objectives: In this paper, we have to establish a generalized common fixed point theorem in cone rectangular metric spaces. Methods: use the Banach contraction principle technique theorem. Findings: The paper presents unique for two weakly compatible self-maps satisfying expansive type mapping space without assuming normality condition of cone. Our result extends and supplements some well-known...

Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...

Abstract In this manuscript, we present a new notion which is named as extended N b -cone metric space over Banach algebra and investigate some fixed point results in the setting. order to examine validity of underlying gave an application for existence uniqueness solution system Fredholm integral equation. At last, interesting examples illustrate our work.

The object of this paper is to introduce the concept of compatibility of pair of self maps in a cone metric space without assuming its normality. Using this concept we establish a unique common fixed point theorem for four self maps satisfying a generalized contractive condition in a cone metric space which generalizes and synthesizes the results of L. G. Huang and X. Zhang [3]( J. Math. Anal. ...

In this paper, we introduce a new concept on a complete generalized D∗-metric space by using the concept of generalized D∗-metric space (D∗-cone metric space) called ∇∗∗-distance and, by using the concept of the ∇∗∗-distance we prove some new fixed point theorems in complete partially ordered generalized D∗-metric space which is the main result of our paper. c ©2015 All rights reserved.

The paper is concerned with the optimal design problems for the fourth order variational inequalities. Namely, the first order necessary optimality conditions are derived for the class of optimization problems under consideration. The differential stability of metric projection in the Sobolev space HQ{Q) onto the cone of nonnegative elements is considered by Mignot [9]. Mignot derived the form ...

The aim of this paper is to establish a unique common fixed point theorem for six self maps satisfying a generalized contractive condition in a cone metric space. The intent of this paper is to introduce the concept of compatibility of pair of self maps in a cone metric space without assuming its normality. Our results generalize, extend and unify several well-known comparable results in the li...