Existence of a solution of integral equations via fixed point theorem
Applying fixed-point theory to establish existence of a solution for an integral equation.
Question
Can the existence of a solution for a nonlinear integral equation be guaranteed under suitable assumptions on the functions involved?
Method
The paper first develops auxiliary fixed-point results and then applies them to the stated integral equation.
- Define the integral equation and continuity assumptions
- Develop auxiliary fixed-point results
- Transfer the theorem to the integral-equation problem
Mathematical model
The integral equation studied in the paper
Findings
The paper establishes existence of a solution for the studied integral equation and uses auxiliary fixed-point results that generalize, improve, and unify earlier theorems.
Why it matters
This is a clear example of the path from a concrete problem to a mathematical model, a suitable analytical tool, and a usable existence result—the same problem-to-model-to-solution pattern relevant to computational work.
Sources and evidence
Have an analytical or computational problem?
Describe the problem and goal so we can discuss a suitable path for modeling, analysis, and implementation.