Generalized Wellposedness and Multivalued Contraction

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In this paper, we establish the fixed point theorem for multivalued contraction. Also we prove that the generalized well posedness of the fixed point problem and continuity of multivalued contraction. 


Fixed point; Multivalued mapping; Well-posedness

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Kannan, R Some results on fixed points, Bull. Calcutta Math.Soc. 10 71-76 1968.

Kunze, H.E., La Torre, D., and Vrscay, E.R., Contractive multifunctions, fixed point inclusions and iterated multifunction systems, J. Math. Anal. Appl. 330:159-173 2007.

Nadler, S.B., Multivalued contraction mappings, Pacific J. Math., 30:475-488 1969.

Petrusel A., Rus.I.A, and Cao. J.C, Well-posdeness in the generalized sense of the fixed point problems for multivalued operators, Taiwanese Journal of Mathematics, 11(3) 903-914 2007.

Rhoades, B, E., A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226:257-290 1977. [6]. Rhoades, B.E., Contractive continuity, Contemporary Mathematics, 72 233-245 1988. definitions and

Rhoades, B.E., Fixed points and continuity for multivalued mappings, Internat. J. Math. Math. Sci., 15 15-30 1992.