SOME HYBRID FIXED POINT THEOREMS FOR PARTIAL CONTRACTION MAPPINGS IN AN ORDERED EUCLIDEAN SPACE ℝn
By
Janhavi B. Dhage and Bapurao C. Dhage
Kasubai, Gurukul Colony, Thodga Road, Ahmedpur,
Distr. Latur, Maharashtra, India-413515
Email: jbdhage@gmail.com, bcdhage@gmail.com
(Received: March 22, 2025; In format: April 05, 2025; Revised: June 04, 2025; Accepted: June 24, 2025)
DOI: https://doi.org/10.58250/jnanabha.2025.55122
Abstract
n this paper we prove two fixed point theorems for linear partial Banach contraction and partial Kannan contraction mappings T in an Euclidean space ℝn via calculus method and using the max/mini principle. It is shown that though our theoretical approach to partial contraction mappings is different from the constructive one, we are not far away from the usual constructive method. Actually one can take an arbitrary point x0 ∈ ℝn which is comparable to Tx0 and if we define a sequence {xn}of iterates of the mapping under consideration, then it is shown that the sequence {xn}converges to a unique comparable fixed point monotonically and geometrically.
2020 Mathematical Sciences Classification: Primary 45G10; Secondary 47H10
Keywords and Phrases: Partially ordered Euclidean space; Max/mini principle; Partial contraction mapping; Hybrid fixed point theorem.