In this paper we obtain some sufficient conditions for the existence of common fixed points of multivalued mappings satisfying generalized contractive conditions in non normal cone metric spaces. These results establish some of the most general common fixed point theorems for two multivalued maps in cone metric spaces. AMS subject classifications: 47H10, 54H25, 54C60, 46B40

In this paper, we introduce the M-cone metric space over Banach algebra as a generalization of both M-metric and cone investigate some fixed point results in new settings. Some examples are presented illustrations. Finally, supported by an application to examine existence uniqueness solution for Fredholm integral equation.

In this survey, we review many examples on cone metric spaces to verify some properties of cones on real Banach spaces and in the sequel, we shall present other examples in cone metric spaces that some properties are incorrect in these spaces but hold in ordinary case like as comparison test.

In this work, we first introduce almost contraction mappings for a pair of two in cone metric spaces over Banach algebras (CMSBA). Then, observe that the class such setting contains those many well known mappings. Finally, prove some fixed point theorems, and obtain $(S,T)$-stability results Jungck iterations CMSBA.

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...

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.

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 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 ...