In this paper, we prove some common fixed-point theorems for two self-mappings in the context of a complete b-metric space by proposing a new contractive type condition. Further, we derive a result for three self-mappings in the same setting. We provide two examples to demonstrate the validity of the obtained results.

In this article, the notion of rational interpolative Meir-Keeler type contraction is discussed. The existence and uniqueness of a fixed point for interpolative Meir-Keeler contraction of rational Das-Gupta are investigated. The obtained results improve and generalize the existing results on the topic in the recent literature.

Let $X$ and $Y$ be affine nonsingular real algebraic varieties. One of the classical problems in real algebraic geometry is whether a given $C^\infty$ mapping $f:X\rightarrow Y$ can be approximated by entire rational mappings in the space of $C^\infty$ mappings. In this work, we obtain some sufficient conditions in the case when $Y$ is the standard sphere $S^n$ .