On best proximity pair theorems and fixed-point theorems
نویسندگان
چکیده
منابع مشابه
On Best Proximity Pair Theorems and Fixed-point Theorems
The significance of fixed-point theory stems from the fact that it furnishes a unified approach and constitutes an important tool in solving equations which are not necessarily linear. On the other hand, if the fixed-point equation Tx = x does not possess a solution, it is contemplated to resolve a problem of finding an element x such that x is in proximity to Tx in some sense. Best proximity p...
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This paper is concerned with the best proximity pair problem in Hilbert spaces. Given two subsets $A$ and $B$ of a Hilbert space $H$ and the set-valued maps $F:A o 2^ B$ and $G:A_0 o 2^{A_0}$, where $A_0={xin A: |x-y|=d(A,B)~~~mbox{for some}~~~ yin B}$, best proximity pair theorems provide sufficient conditions that ensure the existence of an $x_0in A$ such that $$d(G(x_0),F(x_0))=d(A,B).$$
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In this paper, we introduce some new classes of proximal contraction mappings and establish best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...
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In this paper, first we introduce the notion of $frac{1}{2}$-modular metric spaces and weak $(alpha,Theta)$-$omega$-contractions in this spaces and we establish some results of best proximity points. Finally, as consequences of these theorems, we derive best proximity point theorems in modular metric spaces endowed with a graph and in partially ordered metric spaces. We present an ex...
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In this work, we first introduce the concept of approximate sequence and establish some new convergence theorems for approximate sequences. By applying our new convergence theorems, we obtain new best proximity point theorems which improve and generalize some known results in the literature. As applications, some simultaneous generalizations of common fixed point theorems of Banach type, Kannan...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2003
ISSN: 1085-3375,1687-0409
DOI: 10.1155/s1085337503209064