In this present paper, inspired by the concept of weakly CONTRACTIVE MAPPING in metric spaces, we introduce the concept of weakly CONTRACTIVE MAPPING in generalized asymmetric metric spaces and we establish various fixed point theorems for such MAPPINGs in complete generalized metric spaces.

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.

The aim of this paper is to establish certain new classes of proximal contraction MAPPINGs and establish some bestproximity point theorems for such kinds of MAPPING, thereby we extend some fixed point theorems for generalizedweakly CONTRACTIVE MAPPINGs in metric spaces to the case of non-self MAPPING.

In this paper, we prove some results on complex partial b-metric space (Ɽ, , pcb ), which are more generalization of S-CONTRACTIVE MAPPINGs. Also, we expand weakly increasing MAPPINGs of S-CONTRACTIVE for two self-MAPPINGs and prove some common fixed point theorems with supported examples in complete partial b-metric spaces (Ɽ, , pcb ).

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.