منابع مشابه
Best proximity point theorems in 1/2−modular metric spaces
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 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...
متن کاملPythagorean Property and Best-Proximity Point Theorems
The aim of this paper is to prove the existence and convergence theorems for cyclic contractions. We introduce a notion called proximally complete pair (A,B) on a metric space, which unify the earlier notions that are used to prove the existence of a best proximity point for a cyclic contraction. By observing geometrical properties on a Hilbert space, we introduce Pythagorean property and use t...
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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...
متن کاملBest proximity pair and coincidence point theorems for nonexpansive set-valued maps in Hilbert spaces
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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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2011
ISSN: 0021-9045
DOI: 10.1016/j.jat.2011.06.012