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- W1598405890 abstract "Abstract. In this paper we establish new flxed point theorems for modular spaces.AMS subject classiflcations: 46A32Key words: modular space, non-expansive mapping, Fatou property, ¢ 2 -condition, Musi-elak-Orlicz space 1. Introduction The theory of modular space was initiated by Nakano [5] in connection with thetheory of order spaces and redeflned and generalized by Musielak ans Orlicz [4].By deflning a norm, particular Banach spaces of functions can be considered. Met-ric flxed theory for these Banach spaces of functions has been widely studied (see[1]). Another direction is based on considering an abstractly given functional whichcontrols the growth of the functions. Eventhough a metric is not deflned, many prob-lems in flxed point theory for nonexpansive mappings can be formulated in modularspaces.In this paper, a flxed point theorem for nonlinear contraction in the modular spaceis proved. In order to do this, for the sake of convenience, some deflnitions andnotations are recalled from [2, 3, 4, 5] and [8].Deflnition 1." @default.
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- W1598405890 date "2011-06-10" @default.
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- W1598405890 title "Fixed point theorems in modular spaces" @default.
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