39Bxx Functional equations and inequalities
This subtopic studies functional equations and inequalities, emphasizing structural properties, solution methods, and the role of symmetry and regularity conditions.
Specific topics
39B05 General theory of functional equations and inequalities
Overview
39B05 develops general theory of functional equations and inequalities in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: General theory of functional equations and inequalities
Useful Links
Key Ideas
- Foundational definitions and model statements for general theory of functional equations and inequalities
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B12 Iteration theory, iterative and composite equations
Overview
39B12 develops iteration theory, iterative and composite equations in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Iteration theory, iterative and composite equations
Useful Links
Key Ideas
- Foundational definitions and model statements for iteration theory, iterative and composite equations
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B22 Equations for real functions
Overview
39B22 develops equations for real functions in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Equations for real functions
Useful Links
Key Ideas
- Foundational definitions and model statements for equations for real functions
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B32 Equations for complex functions
Overview
39B32 develops equations for complex functions in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Equations for complex functions
Useful Links
Key Ideas
- Foundational definitions and model statements for equations for complex functions
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B42 Matrix and operator equations
Overview
39B42 develops matrix and operator equations in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Matrix and operator equations
Useful Links
Key Ideas
- Foundational definitions and model statements for matrix and operator equations
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B52 Equations for functions with more general domains and/or ranges
Overview
39B52 develops equations for functions with more general domains and/or ranges in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Equations for functions with more general domains and/or ranges
Useful Links
Key Ideas
- Foundational definitions and model statements for equations for functions with more general domains and/or ranges
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B55 Orthogonal additivity and other conditional equations
Overview
39B55 develops orthogonal additivity and other conditional equations in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Orthogonal additivity and other conditional equations
Useful Links
Key Ideas
- Foundational definitions and model statements for orthogonal additivity and other conditional equations
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B62 Functional inequalities, including subadditivity, convexity, etc.
Overview
39B62 develops functional inequalities, including subadditivity, convexity, etc. in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Functional inequalities, including subadditivity, convexity, etc.
Useful Links
Key Ideas
- Foundational definitions and model statements for functional inequalities, including subadditivity, convexity, etc.
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B72 Systems of functional equations and inequalities
Overview
39B72 develops systems of functional equations and inequalities in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Systems of functional equations and inequalities
Useful Links
Key Ideas
- Foundational definitions and model statements for systems of functional equations and inequalities
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B82 Stability, separation, extension, and related topics for functional equations
Overview
39B82 develops stability, separation, extension, and related topics for functional equations in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: Stability, separation, extension, and related topics for functional equations
Useful Links
Key Ideas
- Foundational definitions and model statements for stability, separation, extension, and related topics for functional equations
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks
39B99 None of the above
Overview
39B99 develops none of the above in functional equations and inequalities. Core themes include criteria for convergence behavior, structural inequalities, and summability principles used to characterize limiting behavior of sequences and series.
Related Wikipedia Page
Wikipedia search: None of the above
Useful Links
Key Ideas
- Foundational definitions and model statements for none of the above
- Convergence, summability, and asymptotic behavior criteria
- Comparison, transform, and Tauberian-style techniques for proving direct results
Typical Uses
Used to prove convergence or divergence under weakened hypotheses, compare summation methods, and transfer results between sequence spaces and functional-analytic formulations.
Applications
- Asymptotic analysis of numerical and analytic approximation procedures
- Regularization and summation of series in analysis and applied mathematics
- Stability and convergence assessments in iterative and discretized models
References
Recommended Textbooks