arXiv subjects

Sahil Billawria

Publications and source records attributed to Sahil Billawria.

3 recordsLinked to original sources

arXiv2026

Another Perspective on Chatterjea Contraction

Inspired by the well-known result stating that if any iterate of a mapping is a Banach contraction on a complete metric space, then the mapping itself possesses a unique fixed point, we investigate that claim for a Chatterjea contraction but by retaining the left-hand side of the inequality as per the mapping itself. With an additional assumption of k- continuity, the existence and uniqueness of a fixed point is obtained for a new class of contractions, m-Chatterjea contraction, on a complete metric space. Several examples are given in order to substantiate many theoretical claims such as discontinuity at the unique limit point of the iterative sequence, as well as examples demonstrating that this new class strictly contains the class of Chatterjea mappings.

math.FA↗

arXiv2025

Some Fixed Point Theorems in $(α,β)$- Metric Spaces with applications to Fredholm integral and non-linear differential equations

In this paper, we presented a new type of metric space called $(α,β)$-metric space along with some novel contraction mappings named $(α,β)$-contraction and weak $(α,β)$-contraction mapping. We established some fixed point theorem for these newly introduced contractive mappings. Our results extended some fixed point results in the existing literature. We also provide an example which holds for the weak $(α,β)$-contraction. Furthermore, we proved Kannan's fixed point theorem and Reich's fixed point theorem in the setting of $(α,β)$-metric spaces. At the end, as applications the Fredholm integral and non-linear differential equations are solved in order to validate the theoretically obtained conclusions

math.FA↗

arXiv2022

Arzela Ascoli Theorem in Quasi Cone Metric Space

In this paper we investigate Arzela Ascoli Theorem in quasi cone metric space, which is a generalization of metric space. We prove some interesting results using forward and backward toplologies, forward and backward continuity and forward and backward totally boundedness. A new notion forward and backward equicontinuity is also introduced.

math.FA↗