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Approximation and fixed point theorems for countable condensing composite maps

  • Donal O'Regan (a1) and Naseer Shahzad (a2)

Abstract

This paper Presents a multivalued version of an approximation result of Ky Fan (Math. Z.112 (1969)) for maps.

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References

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[1]Agarwal, R.P. and O'Regan, D., ‘Fixed points for admissible multimaps’, Dynamic Systems Appl. 11 (2002), 437447.
[2]Carbone, A. and Conti, G., ‘Multivalued maps and existence of best approximations’, J. Approx. Theory 64 (1991), 203208.
[3]Fan, K., ‘Extensions of two fixed point theorems of F.E. Browder’, Math. Z. 112 (1969), 234240.
[4]Fan, K., ‘Some properties of convex sets related to fixed point theorems’, Math. Ann. 266 (1984), 519537.
[5]Ha, C.W., ‘On a minimax inequality of Ky Fan’, Proc. Amer. Math. Soc. 99 (1987), 680682.
[6]Kong, W.B. and Ding, X.P., ‘Approximation theorems and fixed point theorems for multivalued condensing mappings in wedges’, J. Math. Anal. Appl. 167 (1992), 468481.
[7]Lin, T.C., ‘A note on a theorem of Ky Fan’, Canad. Math. Bull. 22 (1979), 513515.
[8]Lin, T.C., Approximation and fixed points for condensing non self maps defined on a sphere, Proc. Amer. Math. Soc. 105 (1989), 6669.
[9]Lin, T.C. and Yen, C.L., ‘Applications of the proximity map to fixed point theorems in Hilbert spaces’, J. Approx. Theory 52 (1988), 141148.
[10]Lin, T.C. and Park, S., ‘Approximation and fixed point theorems for condensing composites of multifunctions’, J. Math. Anal. Appl. 223 (1998), 18.
[11]Liu, L.S., ‘Approximation theorems and fixed point theorems for various classes of 1–set contractive mappings in Banach spaces’, Acta Math. Sinica 17 (2001), 103112.
[12]Liu, L.S., ‘On approximation theorems and fixed point theorems for non self mappings in infinite dimensional Banach spaces’, J. Math. Anal. Appl. 188 (1994), 541551.
[13]O'Regan, D., ‘A unified fixed point theory for countably P-concentrative mappings’, Appl. Anal. 81 (2002), 565574.
[14]Park, S., Singh, S.P. and Watson, B., ‘Some fixed point theorems for composites of acyclic maps’, Proc. Amer. Math. Soc. 121 (1994), 11511158.
[15]Reich, S., Approximate selections, ‘best approximations, fixed points and invariant sets’, J. Math. Anal. Appl. 62 (1978), 104113.
[16]Sehgal, V.M. and Singh, S.P., ‘A theorem on the minimization of a condensing multifunction and fixed points’, J. Math. Anal. Appl. 107 (1985), 96102.
[17]Sehgal, V.M. and Singh, S.P., ‘A generalization to multifunctions of Fan's best approximation theorem’, Proc. Amer. Math. Soc. 102 (1988), 534537.
[18]Smart, D.R., Fixed point theory (Cambridge University Press, London, 1974).
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Approximation and fixed point theorems for countable condensing composite maps

  • Donal O'Regan (a1) and Naseer Shahzad (a2)

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