Modified α-ψ-contractive mappings with applications
A study of generalized contractive conditions, fixed-point results, and applications to integral equations.
Question
How can α-ψ contractive conditions be modified to obtain stronger fixed-point theorems and then apply those results to concrete problems such as integral equations?
Method
The paper modifies the notions of α-admissible and α-ψ-contractive mappings and develops fixed-point theorems in complete metric spaces.
- Define and modify the contractive structure
- Prove fixed-point theorems
- Examine examples and applications to integral equations
Mathematical core
The conceptual fixed-point form
The equation above is the compact fixed-point form; the paper develops the contractive conditions needed to guarantee such a point.
Findings
The paper establishes new fixed-point theorems in complete metric spaces and shows how several earlier results follow as special cases. Examples and applications to integral equations are also given.
Why it matters
The useful pattern is methodological: define the structure precisely, derive a provable condition, and then transfer the result to a concrete problem. The same pattern appears in mathematical modeling and algorithm design.
Sources and evidence
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