Fixed Points of Nonlinear and Asymptotic Contractions in the Modular Space
نویسندگان
چکیده
منابع مشابه
Fixed Points of Nonlinear and Asymptotic Contractions in the Modular Space
The theory of modular space was initiated by Nakano [1] in connection with the theory of order spaces and was redefined and generalized byMusielak and Orlicz [2]. By defining a norm, particular Banach spaces of functions can be considered. Metric fixed theory for these Banach spaces of functions has been widely studied (see [3]). Another direction is based on considering and abstractly given fu...
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There are many papers in the literature that discuss the asymptotic fixed point theory, in which the existence of the fixed points is deduced from the assumption on the iterates of an operator (e.g., [1, 6] and the references therein). Recently, Kirk [5] studied an asymptotic fixed point theorem concerning nonlinear contractions. He proved the following theorem [5, Theorem 2.1] by appealing to ...
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In this paper, we discuss the existence and uniqueness of xed points for Banach and Kannancontractions dened on modular spaces endowed with a graph. We do not impose the Δ2-conditionor the Fatou property on the modular spaces to give generalizations of some recent results. Thegiven results play as a modular version of metric xed point results.
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2007
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2007/40575