Abstract of a paper by Mohammad Imdad, Rqeeb Gubran and Md Ahmadullah
This is an announcement for the paper “Using an implicit function to prove common fixed point theorems” by Mohammad Imdad, Rqeeb Gubran and Md Ahmadullah. Abstract: We observe that, Theorem 2 due to Berinde and Vetro (Fixed Point Theory Appl. 2012:105) is not correct in its present form. In this paper, by correcting and enriching aforementioned theorem, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results unify, extend and generalize many relevant results of the existing literature. Interestingly, unlike many other cases, our main results deduce a nonlinear order-theoretic version of a well-known fixed point theorem (proved for quasi-contraction) due to $\'{C}iri\'{c}$ (Proc. Amer. Math. Soc. (54) 267-273, 1974). Finally, in the setting of metric spaces, we drive a sharpened version of Theorem 1 due to Berinde and Vetro (Fixed Point Theory Appl. 2012:105). The paper may be downloaded from the archive by web browser from URL http://arxiv.org/abs/1605.05743
participants (1)
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Bentuo Zheng (bzheng)