Abstract
This paper establishes the existence of fixed points related to strict Chatterjee contractive mappings by relaxing the compactness of the underlying spaces and the continuity of the mapping involved, using altering distance functions and comparison functions in the general setting of metric spaces. Several non-trivial and illustrative examples are provided to demonstrate, support, and validate the obtained theoretical results. In addition, a theorem that can characterize the completeness of metric spaces through the existence of fixed points is rigorously proven and discussed. Furthermore, a theorem on strict Chatterjea-type modulus contractive mappings without continuity assumptions and with relaxed compactness conditions is proposed and analyzed in detail. As a practical and meaningful application, the main theorems are applied to solve mathematical models arising from cantilever beam problems in engineering. The paper concludes by posing two open and challenging research questions intended to stimulate further investigations and promote future research in this important and rapidly developing area of fixed point theory.
Recommended Citation
Singh, Irom Shashikanta and Singh, Y. Mahendra
(2026).
(SI16 No04) Some Fixed Point Theorems On Chatterjea Type Contractions,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 21,
Iss.
3, Article 2.
Available at:
https://digitalcommons.pvamu.edu/aam/vol21/iss3/2