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Research

  My research interest concern the following theories and topics:
- Compactness criteria in functions spaces and applications to the impulsive and/or neutral differential systems.
- Common fixed points theory and applications to differential systems.
- Minimal displacement problem and optimal retraction problem in Banach spaces.
- Iterative methods to approximate fixed points and solutions of variational inequalities in Banach spaces.
- Qualitative and quantitative properties of nonlinear elliptic PDE.

  I am a member of the Gruppo Nazionale di Analisi Matematica, Probabilità e Applicazioni  (G.N.A.M.P.A.) and Unione Matematica Italiana   (U.M.I.).




Publications

  In the sequel I include a list of my scientific publications:
40. (with L. Montoro and B. Sciunzi) Classification of solutions to $-\Delta u=u^{-\gamma}$ in the half-space, to appear in Mathematische Annalen.

39. (with G. Chirillo, L. Montoro and B. Sciunzi) Existence and regularity for a general class of quasilinear elliptic problems involving the Hardy potential, Journal of Differential Equations, 349 (2023), 1-52.

38. (with G. Chirillo, L. Montoro and B. Sciunzi) Symmetry via the moving plane method for a class of quasilinear elliptic problems involving the Hardy potential, Proceedings of the Royal Society of Edinburgh Section A: Mathematics, DOI:10.1017/prm.2022.74 (2022), 1-25.

37. (with V. Colao) Solutions to nonlocal evolution equations governed by non-autonomous forms and demicontinuous nonlinearities, Journal of Evolution Equations, 22 (2022), no. 4, 77.

36. (with V. Colao and H.K. Xu) Mild Solutions of nonlocal semilinear evolution equations on unbounded intervals via approximation solvability method in reflexive Banach spaces, Journal of Mathematical Analysis and Applications, 498 (2021), no. 1, 124938.

35. (with G. Marino) Some results on the approximation of solutions of variational inequalities for multivalued maps on Banach spaces, Mediterranean J. of Math. 18 (2021), no. 4, 1-19.

34. (with H.K. Xu) On Solving Variational Inequalities Defined on Fixed Point Sets of Multivalued Mappings in Banach Spaces, Journal of Fixed Point Theory and Applications, 22 (2020), no. 4, 1-17.

33. (with F. Cianciaruso and P. Pietramala) Coupled elliptic systems depending on the gradient with nonlocal BCs in exterior domains, Boundary Value Problems, 1 (2020), 1-17.

32. (with G. Marino) Boundary point method and Mann-Dotson algorithm for non-self mappings in Banach spaces, Milan Journal of Mathematics, 87 (2019), no. 1, 73-91.

31. (with G. Marino) Boundary point method and Mann-Dotson's algorithm for non-self strict pseudo-contractive mappings in uniformly smooth Banach spaces, Numerical Functional Analysis and Optimization, 40 (2019), no. 7, 844-865.

30. (with G. Marino, N. Hussain and B.A. Alamri) Ergodic type theorems for nonspreading mappings, Journal of Nonlinear and Convex Analysis, 17 (2016), no. 10, 2071-2082.

29. (with V. Colao and H.K. Xu) An existence result for a new class of impulsive functional differential equations with delay, Journal of Mathematical Analysis and Applications, 441 (2016), no. 2, 668-683.

28. (with V. Colao and G. Marino) On approximation of zeros of non-self monotone operators, Numerical Functional Analysis and Optimization, 37 (2016), no. 6, 667-679.

27. (with F. Cianciaruso, G. Marino and H.K. Xu) Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces, Optimization, no. 6, 1259-1275.

26. (with N. Hussain, G. Marino and A. Abdou) On the strong convergence of a general type Krasnosel'skii-Mann's algorithm depending on the coefficients, Journal of Fixed Point Theory and Applications, 18 (2016), 1-25.

25. (with G. Marino) On the role of the coefficients about the strong convergence of a general type Mann iterative scheme, Journal of Inequalities and Applications, (2015) 2015:118.

24. (with V. Colao) A hierarchical approach to fixed point problems for uniformly asymptotically regualar sequences, Journal of Nonlinear and Convex Analysis, 16 (2015), no. 9, 1717-1735.

23. (with N Hussain, G. Marino and B.A. Alamri)  On some Mann's type iterative algorithms, Fixed Point Theory and Applications 2015:17 (3 February 2015) 16pp.

22. (with V. Colao and H.K. Xu)  Existence of solutions for a second order differential equation with non-instantaneous impulses and delay,  Annali di Matematica Pura e Applicata, (4) 195 (2016), no. 3, 697-716.

21. (with G. Marino)  On the auxiliary mappings generated by a family of mappings and solutions of variational inequality problems,  Optimization Letters, (2015), no. 2, 263-282.

20. (with G. Marino and Y. Yao)  The uniform asymptotical regularity of families of mappings and solutions of variational inequality problems,   Journal of Nonlinear and Convex Analysis  15 (2014), no. 3, 477-492.

19. (with  G. Marino and Y. Yao) A modified Korpelevich's method for variational inequalities, Optimization,  63 (2014), no. 4, 559-569.

18. (with P. Pietramala)  A second order impulsive differential equations with functional initial conditions on unbounded intervals,  Journal of Function Spaces and Applications, art. ID 479049 9 pp.

17. (with Y. Yao) A note on implicit and explicit Mann iterative processes for asimptotically ϕ-strongly pseudocontractive mappings, Journal of Applied Mathematics, (2012) art. ID 912150 14pp.

16. (with  G. Marino and X. Wang) On the convergence of Mann and Ishikawa iterative processes for asymptotically $\phi$- strongly pseudocontractive mappings, Abstract and Applied Analysis (2012) art ID. 850104 19pp.

15. (with  V. Colao and G. Marino) On some auxiliary mappings generated by nonexpansive and strictly pseudo-contractive mappings, Applied Mathematics and Computation 218 (2012), no. 11, 6231-6241.

14. (with  G. Marino and Y. Yao) Viscosity methods for common solutions for equilibrium and variational inequality problems via multi-step iterative algorithms and common fixed points, Nonlinear Analysis TMA 75 (2012), no. 4, 1787-1798.

13. (with  F. Cianciaruso, G. Marino and H.K. Xu) Notes on graph convergence for maximal monotone operators, Bull. Australian Math. Soc. 83 (2011), no. 1, 22-29.

12. (with  F. Cianciaruso, G. Marino and Y. Yao) An hybrid projection algorithm for finding solutions of mixed equilibrium problems and variational inequality problems, Fixed Point Theory and  Appl., (2010), art. ID 383740 19 pp.

11. (with  F. Cianciaruso, G. Marino and Y. Yao) On a two-steps algorithm for hierarchical fixed points problems and variational inequalities, Jour. of Inequalities and Appl. vol. 2009, 13 pages, doi:10.1155/2009/208692.

10. (with  F. Cianciaruso, G. Marino and H. Zhou) Strong convergence of viscosity methods for continuous pseudocontractive mappings in Banach spaces, Journal of Applied Analysis and Stoch. Anal. vol. 2008, 11 pages, doi:10.1155/2008/149483.

9. (with  F. Cianciaruso, V. Colao and H.K. Xu) On implicit hierarchical fixed point approach to variational inequalities, Bull. Australian Math. Soc. 80 (2009), no. 1, 117-124.

8. (with  V. Colao and G. Marino) Viscosity methods for common solutions for equilibrium and hierarchical fixed point problems, Optimization 60 (2011), no. 5, 553-573.

7. (with  F. Cianciaruso and G. Marino) Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert spaces, Journal of Optimization Theory and Appl., 146 (2010), no. 2, 491-509.

6. (with  G. Marino, V. Colao and Y. Yao) Krasnoselski-Mann iteration for hierarchical fixed points and equilibrium problem,  Bull. Australian Math. Soc. 79 (2009), no. 2, 187-200.

5. (with  F. Cianciaruso and G. Marino) Ishikawa iterations for equilibrium and fixed point problems for nonexpansive mappings in Hilbert spaces, Fixed Point Theory, 9 (2008), no. 2, 449-464.

4. (with  K. Goebel, G. Marino and R. Volpe) The retraction constant and the minimal displacement characteristic of some Banach spaces, Nonlinear Analysis TMA, 67 (2007), no. 3, 735-744.

3. (with  G. Marino and V. Colao) A note on weakly isotone maps and common solutions for differential systems, Acta Math. Sinica (English series), 22 (2006), no. 4, 1171-1174.

2. (with  G. Marino, and P. Pietramala) Impulsive neutral integrodifferential equations on unbounded intervals, Mediterranean J. of Math., 1 (2004), no. 1, 93-108.

1. (with  G. Marino, and P. Pietramala) Impulsive neutral semilinear equations on unbounded intervals, Nonlinear Functional Anal. and Appl., 9 (2004), no. 4, 527-543.


Optimal retraction problem and solutions of integrodifferential systems, Ph.D. Thesis, Università della Calabria, December 2006.
Conferences and Talks


From July 2002 at today I have taken part to many conferences. In the following I have presented a talk:

(1) September 2003, XVII Congresso dell'Unione Matematica Italiana, "Un risultato di compattezza per lo spazio delle funzioni continue su un intervallo non limitato tranne su un numero         finito di punti in cui hanno una discontinuità di prima specie. Un'applicazione.", Milan (Italy)

(2) June 2004, V Internation Conference on Functional Analysis and Approximation Theory, "About common solutions for differential systems.", Maratea (Italy)

(3) July 2009, Functions spaces IX, "Iterative methods for equilibrium and fixed point problems for nonexpansive semigroups in Hilbert spaces.", Krakow (Poland)

(4) July 2010, International Conference on Fixed Point Theory, Variational Inequality and its Approximation Algorithms, "Viscosity methods for common solutions on equilibrium and variational inequality problems via multi-steps iterative algorithms and common fixed points", Chengdu (PRC)

(5) May 2011, Seminari di Analisi Matematica, " Metodi tipo Mann per interessanti operatori nonlineari", Dipartimento di Matematica, UNICAL

(6) November 2011, International Conference on Analysis and Applications, "Viscosity methods for common solutions on equilibrium and variational inequality problems via multi-steps iterative algorithms and common fixed points", Aligarh Muslim University - Aligarh (India)

(7) July 2012, 10th I.C. on Fixed Point Theory and its Applications, "Some auxiliary mappings generated by families of mappings and solutions of variational inequalities on common fixed points-sets", Babeş-Bolyai University, Cluji-Napoca  (Romania)

 (8) June 2013, Giornata UNICAL dell'Analisi Matematica, "Approximation of common fixed points of family of mappings and solutions of variational inequalities problems", Dipartimento di Matematica, UNICAL

(9) September 2013, Incontro G.I.A.F., "Approssimazione di punti fissi comuni per mappe nonlineari", Dipartimento di Matematica, Università di Genova

 (10) December 2014, Workshop on Nonlinear Analysis and Optimization, "A hierarchical approach to fixed point problems for uniformly asymptotically regular sequences", Department of Applied Mathematics, Kaohsiung  (Taiwan)

 (11) July 2015, Function Spaces XI, "Matrix approaches to regularization of nonlinear mappings", Zielona Gora (Poland)

 (12) July 2015, 11th I.C. on Fixed Point Theory and its Applications , "Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces", Galatasaray University, Istanbul (Turkey)

(13) September 2015, 17th International Symposium on Symbolic and Numeric Algorithms for Scientific Computings , "On the role of the coeffcients on the convergence of general type iterative algorithms", Timisoara University, Timisoara (Romania)

(14) June 2016, Italian-Poland meeting , "Iterations for non-self operators", Marie Curie-Sklodowska University, Lublin (Poland)

(15) April 2017, International Workshop on Mathematical Methods in Engineering, MME-2017 , "Approximantions on non-self monotone operators", Cankaya University, Ankara (Turkey)

(16) August 2017, Recent Trends in Pure and Applied Mathematics , "On the Approximation of Solutions of Variational Inequality Problems via Fixed Point Approaches", "1 Decembrie 1918" University of Alba Iulia, Alba Iulia (Romania)

(17) September 2018, Joint meeteng UMI-SIMAI-PTB , "Approximation of Non-self Monotone Operators", University of Wroclaw, Wroclaw (Poland)

(18) September 2018, Giornate di Equazioni Differenziali Ordinarie (GEDO) 2018 , "An Existence Result for a New Class of Impulsive Functional Differential Equations with Delay", Università di Ancona, Ancona (Italy)

(19) July 2019,  Invited talk , "Boundary point method and Mann-Dotson algorithm for non-self mappings in Banach spaces", Normal University of Shanghai, Shanghai (PRC)

(20) July 2019, 13th I.C. on Fixed Point Theory and its Applications , "Boundary point method and Mann-Dotson algorithm for non-self mappings in Banach spaces", Henan Normal University, XinXiang (PRC)

(21) September 2019, 43rd Annual Meeting of the AMASES , "On the solutions of variational inequality problems on fixed point sets of multivalued mappings on reflexive Banach spaces", Università di Perugia, Perugia

(22) January 2020, Multivariate Approximation: theory and applications , "Boundary point method and Mann-Dotson algorithm for non-self mappings in Banach spaces", Università di Perugia, Perugia

(23) May 2021, Workshop on analysis and applications , "Some results on the approximation of solutions of variational inequalities for multivalued maps on Banach spaces", Università di Perugia.

(24) April 2022, Proprietá qualitative per soluzioni di equazioni ellittiche non-lineari , "On the existence of solutions of semilinear evolution equations on bounded intervals", Università della Calabria, Cosenza

In the conference Functional Analysis: Methods and Applications, July 2008, Amantea (CS), Italy I was member of the Organizing committee.

In the workshop Topics in Differential Problems and Functional Analysis, March 2017, Rende (CS), Italy I was member of the Scientific and Organizing committee.

In the conference International Conference on Nonlinear Analysis and Convex Analysis, July 2017, Hokkaido, Japan I was member of the International program committee.

In the conference International Conference on Nonlinear Analysis and Convex Analysis - International Conference on Optimization: Techniques and Applications, July 2019, Hokodate, Japan I was member of the International Program committee.

In the conference Functional Analysis, Approximation Theory and Numerical Analysis, July 2020, Matera, Italy I am co-organizer of the special session: Methods of functional analysis in approximation problems, differential equations and integral equations.

In the conference Nonlinear PDE in Cosenza , May 2023, Cosenza, Italy I was member of the Organizing committee.