Abstract
In this paper, we introduce and prove a fixed point theorem for \( (\alpha ,\psi ,\xi ) \)-generalized contractive multivalued map**s on collections of non-empty closed subsets. We also prove the \( \xi \)-generalized Ulam-Hyers stability results for fixed point inclusion. Finally, we provide illustrative example to support our main result.
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References
J. von Neumann, Zur theorie der gesellschaftsspiele. Math. Ann. 100(1), 295–320 (1928)
S.B. Nadler Jr, Multivalued contraction map**. Pac. J. Math. 30(2), 475–488 (1969)
R. Kannan, Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71–76 (1968)
I.A. Rus, Generalized Contractions and Applications (Cluj University Press, Cluj-Napoca, 2001)
V. Berinde, On the approximation of fixed points of weak contractive operators. Fixed Point Theory 4(2), 131–142 (2003)
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \( \alpha \)-\( \psi \)-contractive type map**s. Nonlinear Anal. 75, 2154–2165 (2012)
J.H. Asl, S. Rezapour, N. Shahzad, On fixed points of \( \alpha \)-\( \psi \)-contractive multifunctions. Fixed Point Theory Appl. 2012, 212 (2012)
M.U. Ali, T. Kamran, E. Karapınar , \( (\alpha ,\psi ,\xi ) \) -contractive multivalued map**s. Fixed Point Theory Appl. 2014, 7 (2014)
S.M. Ulam, Problems in Modern Mathematics (Wiley, New York, 1964)
D.H. Hyers, On the stability of the linear functional equation. Proc. Natl. Acad. Sci. U.S.A. 27(4), 222–224 (1941)
M.F. Bota-Boriceanu, A. Petruşel, Ulam-Hyers stability for operatorial equations, Analel Univ. Al. I. Cuza, Iaşi, 57, 65–74 (2011)
L. Cădariu, L. Găvruţa, P. Găvruţa, Fixed points and generalized Hyers-Ulam stability. Abstract Appl. Anal. 2012 (712743), 10 (2012)
I.A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances. Fixed Point Theory 9(2), 541–559 (2008)
I.A. Rus, Remarks on Ulam stability of the operatorial equations. Fixed Point Theory 10(2), 305–320 (2009)
W. Sintunavarat, Generalized Ulam-Hyers stability, well-posedness and limit shadowing of fixed point problems for \( \alpha \)-\( \beta \)-contraction map** in metric spaces. Sci. World J. 2014(569174), 7 (2014)
RH. Haghi, M. Postolache, Sh. Rezapour, On \( T \)-stability of the Picard iteration for generalized \( \psi \)-contraction map**s. Abstr. Appl. Anal. 2012(658971), 7 (2012)
S. Phiangsungnoen, P. Kumam, Ulam-Hyers Stability results for fixed point problems via generalized multivalued almost contraction, in Proceedings of the International Multiconference of Engineers and Computer Scientists 2014, pp. 1222–1225 (2014)
Acknowledgments
The authors were supported by the Higher Education Research Promotion and National Research University Project of Thailand, Office of the Higher Education Commission (NRU-CSEC No.55000613).
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Phiangsungnoen, S., Wairojjana, N., Kumam, P. (2015). Fixed Point Theorem and Stability for (α, ψ, ξ)-Generalized Contractive Multivalued Map**s. In: Yang, GC., Ao, SI., Huang, X., Castillo, O. (eds) Transactions on Engineering Technologies. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9588-3_10
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DOI: https://doi.org/10.1007/978-94-017-9588-3_10
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