A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space
نویسندگان
چکیده
منابع مشابه
A Fixed Point Theorem for Mappings Satisfying a Contractive Condition of Rational Type on a Partially Ordered Metric Space
and Applied Analysis 3 Again, using induction d xn 1, xn ≤ ( β 1 − α )n d x1, x0 , 2.5 Put k β/ 1 − α < 1. Moreover, by the triangular inequality, we have, form ≥ n, d xm, xn ≤ d xm, xm−1 d xm−1, xm−2 · · · d xn 1, xn ≤ ( km−1 km−2 · · · k ) d x1, x0 ≤ ( k 1 − k ) d x1, x0 , 2.6 and this proves that d xm, xn → 0 as m,n → ∞. So, {xn} is a Cauchy sequence and, since X is a complete metric space, ...
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2010
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2010/190701