Complex vector functional equations / Ice Risteski, Valéry Covachev.

Includes bibliographical references (pages 319-322) and index.

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The subject of complex vector functional equations is a new area in the theory of functional equations. This monograph provides a systematic overview of the authors' recently obtained results concerning both linear and nonlinear complex vector functional equations, in all aspects of their utilization. It is intended for mathematicians, physicists and engineers who use functional equations in their investigations.

Ch. 1. General classes of cyclic functional equations. 1. Basic cyclic functional equation. 2. Derived cyclic functional equation. 3. Paracyclic functional equation. 4. Semicyclic functional equation. 5. Special cyclic functional equation. 6. Condensed cyclic functional equation -- ch. 2. Functional equations with operations between arguments. 7. Operator functional equation. 8. Generalized functional equation. 9. Simple functional equations. 10. Functional equations with several unknown functions. 11. Frechet's functional equations. 12. Functional equations with two operations -- ch. 3. Functional equations with constant parameters. 13. General parametric functional equation. 14. Special parametric functional equation. 15. Expanded parametric functional equation. 16. General expanded parametric functional equation -- ch. 4. Functional equations with constant coefficients. 17. Matrix equations. 18. Homogeneous functional equations with constant coefficients. 19. Nonhomogeneous functional equations with constant coefficients. 20. Paracyclic functional equations with constant coefficients -- ch. 5. Systems of linear functional equations. 21. Systems in which each equation contains all unknown functions. 22. Systems in which not all equations contain all unknown functions -- ch. 6. Quadratic functional equations. 23. Simple quadratic functional equation. 24. Special quadratic functional equation -- ch. 7. Modified quadratic functional equations. 25. Basic quadratic functional equation. 26. Permuted quadratic functional equation. 27. First modified quadratic functional equation. 28. Second modified quadratic functional equation. 29. Third modified quadratic functional equation -- ch. 8. Expanded quadratic functional equations. 30. Expanded quadratic functional equations with functional arguments. 31. Expanded quadratic functional equations with the same signs between the functions. 32. Expanded quadratic functional equation with alternating signs between the functions. 33. Generalized quadratic functional equation -- ch. 9. Higher order functional equations. 34. Higher order functional equation without parameters. 35. Higher order functional equation with complex parameters. 36. Nonlinear operator functional equation -- ch. 10. Systems of nonlinear functional equations. 37. Systems of quadratic functional equations. 38. Systems of higher order functional equations.

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