非线性压缩下的非线性度量不动点定理
Relation-theoretic metrical fixed point theorems under nonlinear contractions
摘要：
本文在赋以任意二元关系的度量空间（非本质完备）上建立了非线性压缩的不动点定理。我们的结果推广、改进和统一了几个已知的结果，特别是Samet和Turinici [Commun.数学。肛交。13，82-97（2012）]和Alam和Imdad [J.不动点理论应用17（4），693-702（2015）]。有趣的是，推论我们的一个主要结果证明下对称封闭的任何二元关系仍然是一个尖锐的版本的定理由于Samet和Turinici。最后，我们用例子来强调本文证明的结果中实现的改进。
英文摘要：
We establish fixed point theorems for nonlinear contractions on a metric space (not essentially complete) endowed with an arbitrary binary relation. Our results extend, generalize, modify and unify several known results especially those contained in Samet and Turinici [Commun. Math. Anal. 13, 82-97 (2012)] and Alam and Imdad [J. Fixed Point Theory Appl. 17(4), 693-702 (2015)]. Interestingly a corollary to one of our main results proved under symmetric closure of any binary relation remains a sharpened version of a theorem due to Samet and Turinici. Finally, we use examples to highlight the realized improvements in the results proved in this paper.
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