In this paper, we first present some elementary results concerning cone metric spaces over Banach algebras. Next, by using these results and the related ones about c-sequence on cone metric spaces we obtain some new fixed point theorems for the generalized Lipschitz mappings on cone metric spaces over Banach algebras without the assumption of normality. As a consequence, our main results improve and generalize the corresponding results in the recent paper by Liu and Xu (Fixed Point Theory Appl. 2013:320, 2013). MSC: 54H25; 47H10

In this paper, we introduce the concept of cone b-metric space over Banach algebra and present some common fixed point theorems in such spaces. Moreover, we support our results by two examples. In addition, some applications in the solutions of several equations are given to illustrate the usability of the obtained results.

Rectangular cone b-metric spaces over a Banach algebra are introduced as a generalization of metric space and many of its generalizations. Some fixed point theorems are proved in this space and proper examples are provided to establish the validity and superiority of our results. An application to solution of linear equations is given which illustrates the proper application of the results in spaces over Banach algebra.MSC: Primary 47H10; secondary 54H25

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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.

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In this paper, we obtain some sufficient conditions for the existence and uniqueness of point of coincidence by using simulation functions in the context of metric spaces and prove some interesting results. Our results generalize the corresponding results of [5, 8, 13, 14, 16] in several directions. Also, we provide an example which shows that our main result is a proper generalization of the result of Jungck [

The main idea in this article is to establish some fixed and common fixed point results for multivalued H + -type contraction mappings in symmetric spaces. New results are accompanied with illustrative examples. An application of the obtained results to probabilistic spaces is presented.