TITLE:
Extensions of Some Fixed Point Theorems of Generalized Jaggi-Type F-Contractions via λ-Iteration in Cone b-Metric Spaces with Applications to Differential Equations
AUTHORS:
Elvin Rada
KEYWORDS:
Fixed Point, Cone b-Metric Space, Jaggi Contraction, F-Contraction, λ-Iteration, Differential Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.10,
October
15,
2025
ABSTRACT: In this paper, we investigate fixed point results for Jaggi-type F-contractions in the framework of cone b-metric spaces. Motivated by the need for faster convergence in iterative methods, we use our λ-iteration scheme
x
n+1
=
(
λ−1
)
x
n
+T(
x
n
)
λ
for
λ>1
and initial point
x
0
∈X
, which generalizes the classical Picard iteration. We prove that under suitable contractive conditions, the λ-iteration converges strongly to the unique fixed point of the mapping. Furthermore, we show that the presence of the parameter
λ
effectively reduces the contractive constant, thereby accelerating the convergence rate compared to standard iterations. We illustrate the efficiency of the method with examples and an application to boundary value problems for differential equations. These results enrich the theory of fixed point approximations in generalized metric spaces and open new perspectives for nonlinear analysis and numerical algorithms.