In this paper, we present a new fixed point theorem involving non-compactness measures and shifting distance functions. This paper provides a generalization of the famous fixed point theorem of Banach. A fixed point theory is a gorgeous blend of mathematical analysis that explains the conditions under which maps provide excellent solutions. Numerous mathematicians later used this theory to prove their results; see, for example, the Schauder fixed point theorem, the Darbo fixed point theorem, the nonexpansive fixed point theorem, etc. Additionally, we hypothesized that a large number of known fixed point theorems can be simply deduced from the Banach theorem. Finally, we also use this fixed point theorem in Banach space to establish the existence of a solution to a fractional integral equation and to illustrate the results with an example.
Deuri, Bhuban Chandra
(SI10-003) Some New Fixed Point Theorem via Shifting Distance Functions,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 17,
3, Article 6.
Available at: https://digitalcommons.pvamu.edu/aam/vol17/iss3/6