Journal of the Iranian Mathematical Society

Journal of the Iranian Mathematical Society

MODELLING FREE MECHANICAL OSCILLATIONS AS A SECOND-ORDER DIFFERENTIAL EQUATIONS AND EXPLORING NEW RESULTS FIXED POINTS OF LARGE ENRICHED CONTRACTIONS IN CONVEX PROBABILISTIC b-METRIC SPACES

Articles in Press

Document Type : Research Article

Authors
Ehsan Lotfali Ghasab
reza chaharpashlou
Assistant Professor at Jundi-Shapur University of Technology Dezful, Iran
10.30504/jims.2026.577376.1327
Abstract
This study explores a collection of fixed point theorems and the existence of fixed points

for large enriched contractions within convex probabilistic b-metric spaces. We identify the necessary

conditions that guarantee the presence of fixed points for such mappings. The research employs the

extends Manns iteration algorithm to this context. Several intricate examples are presented, and our

principal findings are applied to the investigation of free mechanical oscillations, which are described

by second-order differential equations.
Keywords
b-metric space, fixed point, differential equations
convex, free mechanical oscillations
Journal of the Iranian Mathematical Society

Articles in Press, Accepted Manuscript
Available Online from 11 August 2026