In this paper, the concept of a weak (βB, ψB)-contractive mapping has been introduced within the context of C ∗-algebra valued partial metric space, and existence of fixed point is established by utilizing the C-class function. Further, several non-trivial examples are provided to show the validity of our results and as application of proved result an integral equation is solved.

In this article, we extend some recently fixed point theorems in the setting of G−fuzzy metric spaces. We introduce some new concepts of contractions called γ-contractions and γ-weak contractions. We prove some fixed point theorems for mappings providing γ-contractions and γ-weak contractions. On the other hand, we consider a more general class of auxiliary functions in the contractivity condition.

In this paper, we use the de nition of fuzzy normed spaces given byBag and Samanta and provide four types of fuzzy versions of contraction. We show that these mappings necessarily have unique  xed points in fuzzynormed linear spaces. Moreover we prove that the presented theorems areindeed fuzzy extensions of their classical counterparts.

In this paper, two double sequence iterations for a strongly r-contractive mapping in the modular space are introduced. It is proved that these sequence iterations are strongly convergent to a fixed point of a strongly r-contractive mapping. Finally, some examples are presented to show the novelty of the main result.