The following sections contain selected scientific publications of the author according to his specialization areas.

1. MIXED TYPE PARTIAL DIFFERENTIAL EQUATIONS  

Books Authored

  1. Mixed type Equations and Maximum Principles in fluid dynamics, 1983 , Greece
  2. Applied Analysis : Partial Differential Equations , Vol. II , 2003, Symmetry Publ. , Greece
  3. Lecture Notes on Mixed Type Partial Differential Equations, World Scientific , 144 pp,1990
  4. Counter Examples in Differential Equations and Related Topics, World Scientific , 192 pp,1991

Selected Citations :

•  W. F. Ames ( G I T ) – for the Mathematical Reviews , AMS :

Any analyst is always concerned about good counterexamples to use in lectures and research. Here is a book with a collection of counterexamples in the areas of continuity,differentiability, extrema, existence, uniqueness, stability, regularity, periodicity, etc. They have been collected from a variety of books and journals. The collection should prove useful to analysts interested in the main topic of differential equations. There is a reasonable bibliography and both a subject and an author index. This is a valuable book for students and researchers alike.

•  –G.C.Rota (M.I.T.) for the World Scientific :

The author knows his business : he has chosen the right counterexamples at the right time. The section on plane autonomous systems is particularly felicitous, and should be consulted by whoever teaches elementary differential equations ( some of the examples are really cute and we will use them in our 400-student course next year ). Why can't mathematicians write more books like this one ?

Books Edited

  • Mathematics – Space Technology , Greece ,1980
  • Mathematical Analysis , Teubner–Texte zur Mathematik ,Vol. 79 , 1985
  • Mixed type Equations , Teubner–Texte zur Mathematik , Vol. 90 , 1986
  • Mathematical Equations and Inequalities , Vol. I , Greece ,1999
  • Mathematical Equations and Inequalities , Vol. II , Greece ,1999

Published Papers 

  1. Weak solutions of the Frankl – Morawetz problem in , (with G. Rassias , Th. Rassias) , Tamkang J. Math. 10 (1979) , no. 1 , 81-91
  2. On the Frankl problem of second kind , Tamkang J. Math. 10 (1979) , no. 2 , 231-236
  3. The 3-dimensional Frankl problem , Bull. Soc. Roy. Sci. Liege 48 (1979) , no. 11-12 , 422-423
  4. The Bitsadze-Lavrentjev problem , Bull. Soc. Roy. Sci. Liege 48 (1979) , no. 11-12 , 424-425
  5. A new mixed type boundary value problem , Bull. Soc. Roy. Sci. Liege 48 (1979) , no. 11-12 , 420-421
  6. The survey on equations of mixed type , “Functional differential systems and related topics” (Proc. First Internat. Conf. , B \ I a\.zejewko,1979) , 295-301 , Higher College Engrg. , Zielona Gora , (1980)
  7. A maximum principle in R^3 , C. R. Math. Rep. Acad. Sci. Canada 2 (1980) , no.3, 131-133
  8. New uniqueness theorems , Bull. Acad. Polon. Sci. Ser. Sci. Math. 28 (1980) , no. 11-12 , 569-571
  9. A new bi-hyperbolic boundary value problem in the Euclidean space , Bull. Acad. Polon. Sci. Ser. Sci. Math. 28 (1980) , no. 11-12 , 565-568
  10. On a defective theorem on elliptic – hyperbolic equations , Bull. Soc. Roy. Sci. Liege 49 (1980) , no. 9-10 , 307-309
  11. Weak solutions for a mixed type problem , Bull. Soc. Roy. Sci. Liege 49 (1980) , no. 5-8 , 278-280
  12. On a Goursat type problem ,C. R. Math. Rep. Acad. Sci. Canada 2 (1980/81) , no. 1 , 49-51
  13. Uniqueness and existence theorems for a mixed type equation , Tamkang J. Math. 12 , (1981) , no. 1 , 77-83
  14. A new mixed type boundary value problem , Bull. Sci. Math. (2) 105 (1981) , no. 3 , 329-336
  15. Mixed type partial differential equations in R^n , Tamkang J. Math. 12 (1981), no. 2 , 177-181
  16. A uniqueness theorem for the generalized Frankl-Tricomi problem , Bull. Sci. Math. (2) 105 (1981) , no. 3 , 321-327
  17. A maximum principle in , J. Math. Anal. Appl. 85 (1982), no. 1, 106-113
  18. Weak solutions of the Frankl problem in the 4- dimensional Euclidean space , Bull. Acad. Polon. Sci. Ser. Sci. Math. 30 (1982) , no. 3-4 , 123-130
  19. An application of the theory of positive symmetric systems to a degenerate multidimensional hyperbolic equation in R^3 ,Serdica 8 (1982), no. 3 , 235-242
  20. An extended Chaplygin problem and a uniqueness theorem for the Chaplygin - Frankl problem , Bull. Soc. Roy. Sci. Liege 51 (1982) , no. 3-4 , 156-160
  21. The Bi-hyperbolic Degenerate Boundary Value Problem in R^3 , Discuss. Math., Vol. 5 , (1982), 101-104
  22. The extended Bitsadze-Lavrentjev-Tricomi boundary value problem , Rend. Circ. Mat. Palermo (2) 33 (1984) , no.2 , 255-264
  23. On the Tricomi problem with two parabolic lines of degeneracy , Bull. Inst. Math. Acad. Sinica 12 (1984) , no. 1 , 51-56
  24. On the exterior mixed type boundary value problem in the Euclidean plane , “Mathematical Analysis” , 269-284 , Teubner-Texte Math. , 79 , Teubner , Leipzig , (1985)
  25. Extended Bitsadze-Lavrentjev problem with two parabolic lines of degeneracy and two elliptic arcs in Euclidean plane , C. R. Acad. Bulgare Sci. 38 (1985) , no. 1 , 31-34
  26. The mixed Bitsadze-Lavrentjev-Tricomi boundary value problem , “Mixed Type Equations” , 6-21 , Teubner-Texte Math. , 90 , Teubner , Leipzig, (1986)
  27. On three new uniqueness theorems of the Tricomi probem for nonlinear mixed type equations , “Mixed Type Equations” , 269-279 , Teubner-Texte Math. , 90 , Teubner , Leipzig, (1986) The mixed Bitsadze-Lavrentjev-Tricomi boundary value problem , J. Math. Res. Expositions 7 (1987) ,no.1 , 77-80
  28. On three new generalized uniqueness theorems of the Tricomi problem for nonlinear mixed type equations , J. Math. Phys. Sci. 22 (1988), no. 6, 681-695
  29. On the well-posedness of the extended Chaplygin problem in a multidimensional region , C. R. Acad. Bulgare Sci. 41 (1988), no. 2 , 35-37
  30. The well-posed Tricomi-Bitsadze-Lavrentjev problem in the Euclidean plane , Atti Accad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 124 (1990) , no. 3-4 , 73-83
  31. The exterior Tricomi and Frankl problem , J. Math. Res. Exposition 10 (1990) no. 4 , 485-493
  32. On the well-posedness of the extended Tricomi-Chaplygin-Frankl problem in a multidimenional region , Chinese. J. Math. 19 (1991) , no.3 , 187-203
  33. On the well-posed Tricomi problem in R^2 , Discuss. Math. 12 (1992) , 85-93
  34. The well-posed Tricomi problem of two kinds , J. Math. Phys. Sci. 27 (1993), no. 6 , 383-393 World Sci. Publishing, River Edge, NJ , (1994)
  35. The well-posed Tricomi problem in the Euclidean plane , “Geometry, Analysis and Mechanics” , 189-195 , World Sci. Publishing, River Edge, NJ , (1994)
  36. Uniqueness of quasi–regular solutions for a parabolic elliptic–hyperbolic Tricomi problem , Bull. Inst. Math. Acad. Sinica 25 (1997) , no.4 , 277-287
  37. Bitsadze-Lavrentjev Problem , Encyclopaedia of Mathematics , Kluwer Academic Publishers , file: B: rassi 1 , March 28 , (1997) , 1-4 , The Netherlands Existence of weak solutions for a parabolic elliptic-hyperbolic Tricomi problem , Tsukuba J. Math. 23 (1999) , no. 1 , 37-54
  38. Uniqueness of quasi-regular solutions for a bi-parabolic elliptic bi-hyperbolic Tricomi problem , Complex Var. Theory Appl.(Taylor & Francis) 47 (2002) , no. 8 , 707-718

 

2. FUNCTIONAL EQUATIONS AND INEQUALITIES 

Books Authored

1. Mathematical Analysis : Multivariable Calculus , Vol. III , 1996 , Symmetry Publ. , Greece

Books Edited
  • Functional Analysis , Approximation Theory and Numerical Analysis , World Scientific , 340 pp,1994
  • Geometry , Analysis and Mechanics , World Scientific ,388 pp,1995
  • Advances in Equations and Inequalities , Hadronic Press , USA , 1999
  • Mathematical Equations and Inequalities , Vol. I , Greece ,1999
  • Mathematical Equations and Inequalities , Vol. II , Greece ,1999  

Published Papers

  1.  On approximation of approximately linear mappings by linear mappings , J. Funct. Anal. 46 (1982) , no. 1 , 126-130
  2. On approximation of approximately linear mappings by linear mappings , Bull. Sci. Math. (2) 108 (1984) , no. 4 , 445-446
  3. On a new approximation of approximately linear mappings by linear mappings , Discuss. Math. 7 (1985) , 193-196
  4. Solution of a problem of Ulam , J. Approx. Theory 57 (1989), no. 3, 268-273
  5. Solution of a stability problem of Ulam , Discuss. Math. 12 (1992) , 95-103
  6. On the stability of the Euler-Lagrange functional equation , Chinese J. Math. 20 (1992) , no. 2 , 185-190
  7. Stefan Banach , Alexander Markowic Ostrowski , Stanislaw Marcin Ulam , “Functional analysis, approximation theory and numerical analysis”, 241-249, World Sci. Publishing, River Edge, NJ , (1994)
  8. Complete solution of the multi – dimensional problem of Ulam , Discuss. Math. 14 (1994) , 101-107
  9. On the stability of the multi-dimensional nonlinear Euler-Lagrange functional equation , “Geometry,Analysis and Mechanics” , 275-285 , World Sci. Publishing, River Edge , NJ , (1994)
  10. On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces , J. Math. Phys. Sci. 28 (1994) , no.5 , 231-235
  11. On the stability of a multi-dimensional Cauchy type functional equation , “Geometry, Analysis and Mechanics” , 365-376 , World Sci. Publishing, River Edge, NJ , (1994)
  12. Solution of a stability problem of Ulam , “Functional analysis, approximation theory and numerical analysis” , 241-249 , World Sci. Publishing, River Edge, NJ , (1994)
  13. On the stability of the general Euler – Lagrange functional equation , Demonstratio Math. 29 (1996) , no. 4 , 755-766
  14. Solution of the Ulam stability problem for Euler-Lagrange quadratic mappings , J. Math. Anal. Appl. 220 (1998) , no. 2 , 613-639
  15. Solution of the Ulam stability problem for quartic mappings , Glasnik Matematicki Ser. III 34 (54) (1999) , no. 2 , 243-252
  16. On the stability of the multi-dimensional Euler-Lagrange functional equation, J. Indian Math. Soc. ( N. S. ) 66 (1999) , no. 1-4 , 1-9
  17. 17. Solution of the General Dth Degree Functional equation , (A.E.I. : Advances in Equations and Inequalities) , Hadronic Press , Fl. , USA , (1999) ,185-189
  18. Generalization of the Euler Theorem to Heptagons leading to a Quadratic Vector Identity , (A.E.I. : Advances in Equations and Inequalities) , Hadronic Press , Fl. , USA , (1999) ,179-183
  19. Augustin Louis Cauchy , His Life and His Work , (A.E.I. : Advances in Equations and Inequalities) , Hadronic Press , Fl. , USA , (1999) ,1-25
  20. On the Euler stability problem , J. Indian Math. Soc. ( N.S. ) 67 (2000) , no.1-4 , 1-15
  21. Solution of the Ulam stability problem for nonlinear five-dimensional Euler quadratic mappings , Southeast Asian Bull. Math. (Springer-Verlag) 24 (2000) , no. 4, 617-621
  22. On approximation of approximately quadratic mappings by quadratic mappings , Ann. Math. Sil. , No. 15 (2001) , 67-78
  23. Solution of a quadratic stability Hyers-Ulam type problem , Ricerche Mat. 50 (2001) , no. 1 , 9-17
  24. Solution of a Cauchy – Jensen stability Ulam type problem , Archivum Mathematicum ( Brno ) 37 (2001) , no.3 , 161-177
  25. Solution of the Ulam stability problem for cubic mappings , Glasnik Matematicki Ser. III 36 (56) (2001) , no.1 , 63-72
  26. Hyers–Ulam stability for a quadratic functional equation in several variables , J. Indian Math. Soc. ( N. S. ) 68 (2001) , no.1-4, 65 - 73
  27. On the Ulam stability of mixed type mappings on restricted domains , J. Math. Anal. Appl. 276 (2002) , no. 2 , 747-762
  28. On the Hyers-Ulam stability problem for quadratic multi-dimensional mappings , Aequationes Math .(Birkhauser-Verlag ) 64 (2002) , no.1-2 , 62-69
  29. Solution of the Ulam stability problem for an Euler type quadratic functional equation , Southeast Asian Bull. Math. 26 (2002) , 101-112
  30. On the Hyers-Ulam stability problem for quadratic multi-dimensional mappings on the Gaussian plane , Southeast Asian Bull. Math. 26 (2002) , 483-502
  31. On some approximately quadratic mappings being exactly quadratic , (with M. J. Rassias) , J. Ind. Math. Soc. 69 (2002) , 155-160.
  32. On the Ulam stability of Jensen and Jensen type mappings on restricted domains , (with M. J. Rassias), J. Math. Anal. Appl. 281 (2003),516-524
  33. On the quadratic functional inequality involving a sum of powers of norms , Intern. J. Math. Sciences 2 (2003) , no. 1 , 173-184
  34. On the general quadratic functional equation , Libertas Math. , 23(2003),165-174.
  35. Solution of a quadratic stability Ulam type problem , Archivum Mathematicum 40( 2004) , 1-16 pp. (.pdf file)
  36. The Ulam stability problem on approximation of approximately quadraticmappings by quadratic mappings, J. Inequ. Pure & Appl. Math. 5(2004), Issue, 1-9pp.
  37. Asymptotic behavior of mixed type functional equations, Austr. J. Math. Anal. and Appl. 1(2004), 1-21pp.
  38. Asymptotic behavior of Jensen and Jensen type functional equations, (with M. J. Rassias), PanAmerican Math. J. 15(2005), No4, 21-35.
  39. Asymptotic behavior of alternative Jensen and Jensen type functional equations, (with M. J. Rassias),Bulletin Sciences Mathematiques 129(2005), Issue 7, 545-558pp.
  40. Alternative Contraction Principle and Ulam Stability Problem, Math. Sci. Res J. 9(7) 2005 190-199pp.
  41. Solution of the Hyers-Ulam stability problem for quadratic type functional equations in several variables, Austral. J. Math. Anal. –electronic 2(2005), Issue 2, 1-9 pp.
  42. On the general quadratic functional equation, Bol. Soc. Mat. Mexicana (3)11(2005), 259-268 pp.
  43. On the Ulam problem for Euler quadratic mappings, Novi Sad J. Math. 35(2)(2005), 57-66.
  44. On the Cauchy-Ulam stability of the Jensen equation in C*-algebras, Internat. J. Pure & Appl. Math. Sci. 2(1)(2005), 92-101.
  45. Alternative contraction principle and alternative Jensen and Jensen type mappings, Internat. J. Appl. Math. & Stat. 4(M06)(2006), 1-10.
  46. Refined Hyers - Ulam approximation of approximately Jensen type mappings, Bulletin Sci. Math. (Article in press) (2006), 1-10.

 

3. OPERATOR THEORY

Books Authored

  • Applied Analysis : Partial Differential Equations , Vol. II , 2003 , Symmetry Publ. , Greece

Books Edited

  • Mathematical Analysis , Teubner–Texte zur Mathematik ,Vol. 79 , 1985
  • Functional Analysis , Approximation Theory and Numerical Analysis , World Scientific , 340 pp,1994
  • Geometry , Analysis and Mechanics , World Scientific ,388 pp,1995
  • Mathematical Equations and Inequalities , Vol. I , Greece ,1999
  • Mathematical Equations and Inequalities , Vol. II , Greece ,1999

Published Papers

  1. Some fixed point theorems in nonlinear analysis , (with G. Rassias , Th. Rassias) “Functional differential systems and related topics”(Proc. First Internat. Conf., B \ I a\.zejewko,1979) , 302-305, Higher College Engrg. , Zielona Gora (1980) 445-446
  2. On the generalized Cesaro operators , Mathematical Analysis , 32-34 , Teubner-Texte Math. , 79, Teubner , Leipzig, (1985)
  3. Landau's type inequalities , C. R. Acad. Bulgare. Sci. 46 (1993) , no.10, 9-11
  4. Open problems in analysis , “Geometry , analysis and mechanics” , 355-364 , World Scientific Publshing Co. , Inc., River Edge, NJ , (1994)
  5. Stefan Banach , Alexander Markowic Ostrowski , Stanislaw Marcin Ulam , “Functional analysis, approximation theory and numerical analysis”, 241-249, World Sci. Publishing, River Edge, NJ , (1994)
  6. New Landau's type inequalities , Discuss. Math. 14 (1994) , 77-99
  7. Fractional linear algebra , “Geometry, Analysis and Mechanics” , 251-267 , World Sci. Publishing, River Edge, NJ , (1994)
  8. Multi-dimensional Landau inequalities ,“Geometry, Analysis and Mechanics” , 287-354 , World Sci. Publishing, River Edge, NJ , (1994)
  9. A new computation formula for the inverse of a matrix , “Geometry, Analysis and Mechanics” , 197-203 , World Sci. Publishing, River Edge, NJ , (1994)
  10. Landau's type inequalities ,“Functional analysis, approximation theory and numerical analysis” , 281-301 , World Sci. Publishing, River Edge, NJ ,(1994)
  11. Generalized Landau's type inequalities , “Functional analysis, approximation theory and numerical analysis” , 303-325 , World Sci. Publishing, River Edge, NJ , (1994)
  12. Landau's type inequalities , J. Math. Anal. Appl. 202 (1996) , no. 1 , 280-301
  13. Multi-dimensional Landau extremum problems , C. R. Acad. Bulgare Sci. 50 (1997) , no. 2 , 5-8
  14. Multi-dimensional Landau extremum problems , J. Indian Math. Soc. ( N. S. ) 66 (1999) , no. 1-4 , 11-16
  15. Six-dimensional Landau inequalities , Demonstratio Math. 32 (1999) , no.2 , 413-431
  16. Mathematical Computation of the Code of a Date , (A.E.I. : Advances in Equations and Inequalities) , Hadronic Press , Fl. , USA , (1999) ,191-210
  17. Augustin Louis Cauchy , His Life and His Work , (A.E.I. : Advances in Equations and Inequalities) , Hadronic Press , Fl. , USA , (1999) ,1-25

 

4. MATHEMATICAL INEQUALITIES

Books Authored
  • Probability Theory and Statistics , 1989 , Symmetry Publ. , Greece
Books Edited
  • Mathematical Equations and Inequalities , Vol. I , Greece ,1999
  • Mathematical Equations and Inequalities , Vol. II , Greece ,1999

Published Papers

  1. A counter example to a conjecture by P. Erdos , (with G. Rassias , Th. Rassias) Proc. Japan Acad. Ser. A Math. Sci. 53 (1977) , no. 4 , 119-121.
  2. Research Problems in Complex Analysis ( New Problem : No. 6.81 ) , (with G. Rassias , Th. Rassias) , ( Eds.: D. A. Bannan and J. G. Clunie , Aspects of Contemp. Complex Analysis) , Acad. Press , (1980) , 584.
  3. On the derivative of a polynomial , Bull. Soc. Roy. Sci. Liege 51 (1982) , no. 9-10 , 379-380.
  4. Two new criteria on characterizations of inner products , Discuss. Math. 9 (1988) , 255-267.
  5. Four new criteria on characterizations of inner products , Discuss. Math. 10 (1990) , 139-146.
  6. Archimedes , “Geometry,Analysis and Mechanics” , 1-4 , World Sci. Publishing, River Edge , NJ , (1994).
  7. On the extended Ostrowski constant , “Functional analysis, approximation theory and numerical analysis” , 237-239 , World Sci. Publishing, River Edge, NJ , (1994).
  8. On the Heisenberg – Pauli – Weyl inequality , J. Inequ. Pure & Appl. Math. 5(2004),Issue 1,1-70 pp.
  9. On the Heisenberg-Weyl Inequality, J.Inequ.Pure and Appl.Math.,6(2004),Issue 1,1-8pp.
  10. On the refined Heisenberg-Weyl type inequality, J.Inequ.Pure & Appl.Math. 6(2005), Issue 2, 1-11pp.
 
 

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