Research
My research interest concern the following
theories and topics:
-Iterative methods to approximate solutions of
variational inequalities and fixed points in Banach spaces.
-Compactness criteria
in functions spaces and applications.
-
Common fixed points theory and applications.
-Boundary value problems for ODEs and PDE.
Publications
In the sequel I include a list of
my scientific publications:
- (
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.
12591275.
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.