In this paper, the quasi-partial b-metric space is defined and general fixed point theorems on this space are discussed with examples. MSC: 47H09; 47H10; 54H25

The aim of this paper was to obtain common fixed point results by using an interpolative contraction condition given by Karapinar in the setting of complete metric space. Here in this paper, we have redefined the Reich–Rus–Ćirić type contraction and Hardy–Rogers type contraction in the framework of quasi-partial b-metric space and proved the corresponding common fixed point theorem by adopting the notion of interpolation. The results are further validated with the application based on them.

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In this paper we introduce the notion of quasi-partial b-metric space and then study coupled fixed point results in a quasi-partial b-metric space. Some examples are also given in support of the obtained results.

The purpose of this study is to introduce a new type of extended metric space, i.e., the rectangular quasi-partial b-metric space, which means a relaxation of the symmetry requirement of metric spaces, by including a real number s in the definition of the rectangular metric space defined by Branciari. Here, we obtain a fixed point theorem for interpolative Rus–Reich–Ćirić contraction mappings in the realm of rectangular quasi-partial b-metric spaces. Furthermore, an example is also illustrated to present the applicability of our result.

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Keywords: Partial b-metric space, quasi-partial b-metric space, quasi-partial b-metric topology, compactness, product quasi-partial b-metric space.Abstract. In this paper we discuss the topological properties of quasi-partial b-metric spaces. The notion of quasi-partial b-metric space was introduced and fixed point theorem and coupled fixed point theorem on this space were studied. Here the concept of quasi-partial b-metric topology is discussed and notion of product of quasi-partial b-metric spaces is also introduced.

In the present research paper, Chatterjea type contraction is defined and discussed in the framework of quasi-partial b-metric space. Further, some common fixed point results are proved using the notion of interpolation. The results are extended to fixed point theorems for modified Chatterjea type Suzuki contraction using w-admissible maps. The results proved are new and unique supported by application which will enrich the existing literature.