fixed point theorems for generalized lipschitzian semigroups
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ID: 133195
2001
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Abstract
Let K be a nonempty subset of a p-uniformly convex Banach space E, G a left reversible semitopological semigroup, and 𝒮={Tt:t∈G} a generalized Lipschitzian
semigroup of K into itself, that is, for s∈G, ‖Tsx−Tsy‖≤as‖x−y‖+bs(‖x−Tsx‖+‖y−Tsy‖)+cs(‖x−Tsy‖+‖y−Tsx‖), for x,y∈K where as,bs,cs>0 such that there exists a t1∈G such that bs+cs<1 for all s≽t1. It is proved that if there exists a closed subset C of K such that ⋂sco¯{Ttx:t≽s}⊂C for all x∈K, then 𝒮 with [(α+β)p(αp⋅2p−1−1)/(cp−2p−1βp)⋅Np]1/p<1 has a common fixed point, where α=lim sups(as+bs+cs)/(1-bs-cs) and β=lim sups(2bs+2cs)/(1-bs-cs).
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| Reference Key |
jung2001internationalfixed
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| Authors | ;Jong Soo Jung;Balwant Singh Thakur |
| Journal | structural engineering and mechanics |
| Year | 2001 |
| DOI |
10.1155/S0161171201007426
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| URL | |
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