Ulam-Hyers Stability and Well-posedness of the Fixed Point Problems for Contractive Multi-valued Operator in \(b\)-metric Spaces
R.P. Agarwal, W. Sintunavarat and P. Kumam, PPF dependent fixed point theorems for an (alpha_c)-admissible non-self mapping in the Razumikhin class, Fixed Point Theory Appl. 2013 (2013), Article ID 280.
J.H. Asl, S. Rezapour and N. Shahzad, On fixed points of (alpha)-(psi)-contractive multifunctions, Fixed Point Theory and Applications 2012 (2012), 212.
I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Ulyanovsk Gos. Ped. Inst. 30, 26–37 (1989).
V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint 3 (1993), 3–9.
V. Berinde, Sequences of operators and fixed points in quasimetric spaces, Stud. Univ. Babes-Bolyai, Math. 16 (4) (1996), 23–27.
V. Berinde, Contractii generalizate si aplica¸tii, Editura Club Press 22, Baia Mare (1997).
M. Boriceanu, M. Bota and A. Petru, Multivalued fractals in b-metric spaces, Central European Journal of Mathematics 8 (2) (2010), 367–377.
M. Bota, V. Ilea, E. Karapnar and O. Mle¸sni¸te, On (alpha_*)-(psi)-contractive multi-valued operators in b-metric spaces and applications, Applied Mathematics & Information Sciences 5 (9) (2015), 2611–2620.
M.F. Bota-Boriceanu and A. Petru¸sel, Ulam-Hyers stability for operatorial equations, Analel Univ. Al. I. Cuza, Ia¸si 57 (2011), 65–74.
S. Czerwik, Contraction meppings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1, 5–11 (1993).
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena. 46 (1998), 263–276.
S. Czerwik, K. Dlutek and S.L. Singh, Round-off stability of iteration procedures for operators in b-metric spaces, J. Natur. Phys. Sci. 11 (1997), 87–94.
L. Cadariu, L. Gavruta and P. Gavru¸ta, Fixed points and generalized Hyers-Ulam stability, Abstract Applied Analysis 2012 (2012), Article ID 712743, 10 pages.
R.H. Haghi, M. Postolache and S.H. Rezapour, On T-stability of the Picard iteration for generalized (psi)-contraction mappings, Abstr. Appl. Anal. 2012 (2012), Article ID 658971, 7 pages.
D.H. Hyers, On the stability of the linear functional equation, Proceedings of the National Academy of Sciences of the United States of America 27 (4) (1941), 222–224.
E. Karapinar and B. Samet, Generalized (alpha)-(psi)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012 (2012), Article ID 793486, 17 pages.
S.B. Nadler Jr., Multivalued contraction mapping, Pacific Journal of Mathematics 30 (2), 475–488 (1969).
A. Petrusel, Multivalued weakly Picard operators and applications, Sci. Math. Jpn. 59 (2004), 169–202.
A. Petrusel and I.A. Rus, Well-posedness of the fixed point problem for multivalued operators, in: O. Cârja and I.I. Vrabie (eds.) Applied Analysis and Differential Equations, World Scientific, Hackensack, 295–306 (2007).
A. Petrusel, I.A. Rus and J.-C. Yao, Well-posedness in the generalized sense of the fixed point problems for multivalued operators, Taiwan. J. Math. 11 (2007), 903–914.
S. Phiangsungnoen and P. Pumam, Generalized Ulam-Hyers stability and well-posedness for fixed point equation via (alpha)-admissibility, Fixed Point Theory and Applications 2014 (2014), 418.
S. Phiangsungnoen, W. Sintunavarat and P. Kumam, Common (alpha)-fuzzy fixed point theorems for fuzzy mappings via (beta_F)-admissible pair, Journal of Intelligent & Fuzzy Systems 27 (2014), 2463–2472.
S. Phiangsungnoen,W. Sintunavarat and P. Kumam, Fuzzy fixed point theorems for fuzzy mappings via (alpha)-admissible with applications, Journal of Uncertainty Analysis and Applications 2014 (2014), 2:20.
S. Phiangsungnoen, W. Sintunavarat and P. Kumam, Fixed point results, generalized Ulam-Hyers stability and well-posedness via (alpha)-admissible mappings in b-metric spaces, Fixed Point Theory and Applications 2014 (2014), 188.
I.A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca (2001).
I.A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory 9 (2) (2008), 541–559.
I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory 10 (2) (2009), 305–320.
I.A. Rus, A. Petru¸sel and A. Sîntamarian, Data dependence of the fixed points set of some multivalued weakly Picard operators, Nonlinear Anal. 52 (2003), 1947–1959.
P. Salimi, A. Latif and N. Hussain, Fixed point results for single and set-valued (alpha)-(eta)-(psi)-contractive mappings, Fixed Point Theory Appl. 2013 (2013), 212.
P. Salimi, C. Vetro and P. Vetro, Fixed point theorems for twisted ((alpha,beta))-psi-contractive type mappings and applications, Filomat. 27 (4) (2013), 605–615.
B. Samet, C. Vetro and P. Vetro, Fixed point theorems for (alpha)-(psi)-contractive type mappings, Nonlinear Analysis. 75 (2012), 2154–2165.
S.L. Singh and B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl. 55 (2008), 2512–2520.
W. Sintunavarat, Generalized Ulam-Hyers stability, well-posedness and limit shadowing of fixed point problems for (alpha)-(beta)-contraction mapping in metric spaces, The Scientific World Journal 2014 (2014), Article ID 569174, 7 pages.
S.M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, NY, USA (1964).
- There are currently no refbacks.
eISSN 0975-8607; pISSN 0976-5905