In this paper we introduce a property and use this property to prove some common fixed point theorems in b-metric space. We also give some fixed point results on b-metric spaces endowed with an arbitrary binary relation which can be regarded as consequences of our main results. As applications, we applying our result to prove the existence of a common solution for the following system of integral equations:where a; b 2 R with a < b, x 2 C OEa; b (the set of continuous real functions defined on OEa; b  R) and K 1 ; K 2 W OEa; b OEa; b R ! R are given mappings. Finally, an example is also given in order to illustrate the effectiveness of such result.

In this paper, we introduce the concept of (α, β)-(ψ, ϕ)-contractive mapping in b-metric spaces. We establish some fixed point theorems for such mappings and also give an example supporting our results. Finally, we apply our main results to prove a fixed point theorem involving a cyclic mapping.

In this paper, we introduce the notion of generalized cyclic contraction pairs in b-metric spaces and establish some fixed point theorems for such pairs. Also, we give some examples to illustrate the main results which properly generalizes some results given by some authors in literature. Further, by using the main results, we prove some common fixed point results for generalized contraction pairs in partially ordered b-metric spaces. Our results generalize and improve the result of Shatanawi and Postolache (Fixed Point Theory Appl. 2013:60, 2013 and several well-known results given by some authors in metric and b-metric spaces. MSC: 47H09; 47H10

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The purpose of this work is to introduce new types of contraction mappings in the sense of a multiplicative metric space. Fixed point results for these contraction mappings in multiplicative metric spaces are obtained. Our presented results generalize, extend, and improve results on the topic in the literature. Moreover, our results cannot be directly obtained as a consequence from the corresponding results in metric spaces. We also state some illustrative examples to claim that our results properly generalize some results in the literature. We apply our main results for proving a fixed point theorem involving a cyclic mapping. MSC: 47H09; 47H10