In this article, we introduce the concept of intuitionistic fuzzy double controlled metric spaces that generalizes the concept of intuitionistic fuzzy b-metric spaces. For this purpose, two noncomparable functions are used in triangle inequalities. We generalize the concepts of the Banach contraction principle and fuzzy contractive mappings by giving authentic proof of these mappings in the sense of intuitionistic fuzzy double controlled metric spaces. To validate the superiority of these results, examples are imparted. A possible application to solving integral equations is also set forth towards the end of this work to support the proposed results.

The purpose of this article is to discuss the existence of best proximity points for Pre $\check{\mathrm{s}}$ i $\acute{\mathrm{c}}$ -type nonself operators, say $T:A^k\to B$ . We also give several examples to support our results. As a consequence of our results, we have provided some interesting formulations of Pre $\check{\mathrm{s}}$ i $\acute{\mathrm{c}}$ fixed point results.