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Research

  My research interest concern the following theories and topics:
-Iterative methods to approximate solutions of variational inequalities and fixed points in Banach spaces.
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Compactness criteria in functions spaces and applications.
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Common fixed points theory and applications.
 -Boundary value problems for ODEs and PDE.


  I am member of the Unione Matematica Italiana (U.M.I.) .



Publications

  In the sequel I include a list of my scientific publications:


  1. (

1) (with  E. De Pascale): Discovering the Algebraic Structure on the Metric Injective Envelope of Real Banach  Space, Topology and its Applications 78(1997), 285-292.
2) (with  E. De Pascale): The Hausdorff Measure of Non Hyperconvexity,  Atti Sem. Mat. Fis. Univ. Modena XLVII(1999), 261-267.
3) (with  E. De Pascale and P.P. Zabreiko): Some Remarks on the Newton-Kantorovic Approximations,  Atti Sem. Mat. Fis. Univ. Modena XLVIII(2000), 207-215.
4) (with  E. De Pascale):  The Newton-Kantorovich Approximations for the Nonlinear Integro-Differential Equations of Mixed Type, Ric. Mat. LI, fasc. 2(2002), 249-260.
5) The Newton-Kantorovich Approximations for the Nonlinear Singular Integral Equations, The Journal of Integral Equations and Applications 14, n. 3(Fall 2002), 223-237.
6) (with  E. De Pascale): Newton-Kantorovich Approximations when the Derivative is Holderian: Old and New Results, Numer. Funct. Anal. Optim. 24, n. 7 & 8(2003), 713-723.
7) Convergence Theorems for Newton-like Methods for Operators with Generalized Holder Derivative,  Fixed Point Theory 5, n. 1(2004), 21-35.
8) (with  E. De Pascale): Estimates of Majorizing Sequences in The Newton-Kantorovich Method, Numer. Funct. Anal. Optim. 27, n. 5 & 6(2006), 529-538.
9) (with  E. De Pascale):  Estimates of Majorizing Sequences in the Newton-Kantorovich Method: a Further Improvement, J. Math. Anal. Appl. 322(2006), 329-335.
10) Convergence of Newton-Kantorovich Approximations to an Approximate Zero, Numer. Funct. Anal. Optim. 28, n. 5 & 6(2007), 631-645.
11) (with G. Marino, L. Muglia):  Ishikawa Iterations for Equilibrium and Fixed Points Problems for Nonexpansive Mappings in Hilbert Spaces, Fixed Point Theory 9, n.2(2008), 449-464.
12) (with G. Marino, L. Muglia and Y. Yao): On a Two-Step Algorithm for Hierarchical Fixed Points Problems and Variational Inequalities, J. Inequal. Appl. 2009, Art. ID 208692, 13 pp.
13) (with V. Colao, L. Muglia, H.K. Xu): On an  Implicit Hierarchical Fixed Point Approach to Variational Inequalities, Bull.  Austr. Math. Soc.  80(2009), 117-124.
14)(with G. Marino, X. Wang): Weak and Strong Convergence of the Ishikawa Iterative Process for a Finite Family of Asymptotically Nonexpansive Mappings,  Appl. Math. Comput. 216 no.12 (2010),p. 3558-3567.
15) (with  G. Marino, L. Muglia): Iterative Methods for Equilibrium and Fixed Point Problems for Nonexpansive Semigroups in Hilbert Spaces,  Journal of Optimization Theory and Applications 146 (2010), 491-509.
16) (with  G.Marino, L. Muglia, H. Zhou): Strong Convergence of Viscosity  Methods for Continuous Pseudocontractive Mappings in Banach Spaces,  Journal of Applied Mathematics and Stochastic Analysis 2008, Art. ID 149483, 11 pp.
17) (with G. Marino, L. Muglia, Y. Yao):  A Hybrid Projection Algorithm for Finding Solutions of Mixed Equilibrium Problem and Variational Inequality Problem, Fixed Point Theory and Applications 2010 (2010), 19 pp.
 18
) A Further Journey in the “Terra Incognita'' of the Newton-Kantorovich Method,  Nonlinear Funct. Anal. Appl. 15(2) (2010), 173-183.
19) (with  G. Marino, L. Muglia, H.K. Xu):  Notes on Graph-Convergence for Maximal Monotone Operators, Bull. Aust. Math. Soc. 83 (2011), no. 1, 22-29.
  20) (with V. Colao, G.Marino, H. K. Xu): A Compactness Result for Differentiable Functions with an Application to Boundary Value Problems, Ann. Mat. Pura Appl. Volume
192, Issue 3 (2013), pp. 407-421.
21)  (with G. Marino, A. Rugiano, B. Scardamaglia): On Strong Convergence of Halpern's Method using Averaged Type Mappings. Journal of Applied Mathematics Volume 2014 (2014),
Article ID 473243, 11 pages.
22) (with G. Marino, A. Rugiano, B. Scardamaglia): On Strong Convergence of  Viscosity type Method using Averaged Type Mappings. Journal of Nonlinear and Convex Analysis 65 (2016), no. 6, 1259-1275.
22) (with G. Marino, N. Hussain): Ergodic approximations via matrix regularization approach.. Fixed Point Theory Appl. 2015, 2015:73, 11 pp.
24) (with G. Marino, L. Muglia, H.K. Xu):  Matrix Approaches to  Approximate Solutions of Variational Inequalities in  Hilbert Spaces. Optimization 65 (2016), no. 6, 1259-1275.
1259–1275.

25) (with P. Pietramala):  Multiple Positive solutions of a (p_1,p_2)-Laplacian system with nonlinear BCs.  Boundary Value
Problems 2015, 2015:163 DOI: 10.1186/s13661-015-0415-4.
26) (with G. Infante and  P. Pietramala):  Solutions of perturbed Hammerstein integral equations with applications. Nonlinear Anal. Real World Appl. 33 (2017), 317--347.
27) (with G. Infante and  P. Pietramala):  Nonzero radial solutions for elliptic systems with coupled functional BCs in exterior domains. Submitted, arXiv:1606.09103.
28)(with G. Infante and  P. Pietramala):  Multiple positive radial solutions for Neumann elliptic systems with   gradient dependence.Submitted, arXiv:1711.08269.
29)(with G. Marino, N. Hussain and E. L: Lorens):  Function spaces, fixed points, approximations, and applications [Editorial]. J. Funct. Spaces 2017(2017), 2 pp.













Conferences and Talks



-May 1995, Functional Analysis: Methods and Applications, Camigliatello Silano (CS).
-June 1997, Variational Problems and Applications, Universitą Federico II, Napoli.
-September 1998, CARTEMI-VIII Convegno di Analisi Reale e Teoria della Misura, Maiori.
-September 1999, XVI Congresso Unione Matematica Italiana, Napoli.
-Luglio 2002, CARTEMI-X Convegno di Analisi Reale e Teoria della Misura, Ischia (NA).
-Luglio 2005, 2nd International Workshop on Functional Analysis Methods in Economics and Finance, Cetraro (CS).
-June 2008, Functional Analysis: Methods and Applications, Amantea (CS).
- July 2012, 10th I.C. on Fixed Point Theory and its Applications, where I presented a comunication by the title "Compactness Results for Differentiable Functions and Applications to the Boundary Value Problems via Fixed Point Methods.", Babeş-Bolyai University, Cluji-Napoca, (Romania).
- September 2013, Incontro G.I.A.F., where I presented a comunication by the title "Approccio Matriciale all'Approssimazione di Punti Fissi", Dipartimento di Matematica, Universitą di Genova.

In the conference Functional Analysis: Methods and Applications, July 2008, I was member of the organizing committee.