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BIMSA Computational Math Seminar
BIMSA Computational Math Seminar
A Unified Approach to Non-Unique Fixed Points via Modified C-Class Ciric-Type Contractions
A Unified Approach to Non-Unique Fixed Points via Modified C-Class Ciric-Type Contractions
Organizers
Tahereh Eftekhari
,
Pipi Hu
,
Xin Liang
,
Zhiting Ma
,
Hamid Mofidi
, Chunmei Su
,
Axel G.R. Turnquist
,
Li Wang
,
Fansheng Xiong
,
Shuo Yang
,
Wuyue Yang
Speaker
Omidire Olaoluwa Jeremiah
Time
Wednesday, April 29, 2026 2:00 PM - 3:00 PM
Venue
A3-4-312
Online
Zoom 518 868 7656
(BIMSA)
Abstract
Fixed point theory is central to nonlinear analysis, yet classical results often assume strict contractivity and guarantee uniqueness, limiting applicability to mappings with inherently non-unique fixed points. This paper addresses this gap by introducing a modified C-class function and establishing new non-unique fixed point theorems for Ciric-type mappings in complete metric spaces.
We construct a generalized contractive inequality using a three-variable modified C-class function combined with an altering distance function. Under orbital continuity and orbital completeness, we prove that Picard iteration converges to a fixed point without requiring global Lipschitz conditions or strict contractivity. Carefully designed examples illustrate the sharpness and generality of the framework, strictly extending classical Ciric and Chatterjea contractions as well as hybrid (Φ,ψ)-contractions.
Our main contributions are: (i) a unified framework encompassing classical and generalized C-class contractions, (ii) existence results for non-unique fixed points, (iii) a simple criterion for uniqueness when desired, and (iv) practical validation through nontrivial examples. These results provide a robust foundation for further research in nonlinear operator theory, iterative methods, and applications in optimization and variational problems.
We construct a generalized contractive inequality using a three-variable modified C-class function combined with an altering distance function. Under orbital continuity and orbital completeness, we prove that Picard iteration converges to a fixed point without requiring global Lipschitz conditions or strict contractivity. Carefully designed examples illustrate the sharpness and generality of the framework, strictly extending classical Ciric and Chatterjea contractions as well as hybrid (Φ,ψ)-contractions.
Our main contributions are: (i) a unified framework encompassing classical and generalized C-class contractions, (ii) existence results for non-unique fixed points, (iii) a simple criterion for uniqueness when desired, and (iv) practical validation through nontrivial examples. These results provide a robust foundation for further research in nonlinear operator theory, iterative methods, and applications in optimization and variational problems.