Cone metric spaces and fixed point theorems of T-Kannan contractive mappings
José R. Morales, Edixon Rojas
在完备锥度量空间上，得到了依赖于另一函数的T-Kannan型映象存在唯一不动点的充分条件.
The purpose of this paper is to obtain sufficient conditions for the existence of a unique fixed point of T-Kannan type mappings on complete cone metric spaces depended on another function.
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In this article, we consider Kannan type contractive self-map $T$ on a metric space $(X,d)$ such that \[d(Tx,Ty)<\frac{1}{2}\{d(x,Tx)+d(y,Ty)\} \mbox{ for all } x \neq y \in X, \] and establish some new fixed point results without taking the compactness of $X$ and also without assuming continuity of $T$. Further, we anticipate a result ensuring the completeness of the space $X$ via FPP of this map. Finally, we are able to give an affirmative answer to the open question posed by J. Górnicki [\textit{Fixed point theorems for Kannan type mappings}, J. Fixed Point Theory Appl. 2017]. Apart from th…
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It is well known that fixed point problems of contractive-type mappings defined on cone metric spaces over Banach algebras are not equivalent to those in usual metric spaces (see [3] and [10]). In this framework, the novelty of the present paper represents the development of some fixed point results regarding sequences of contractions in the setting of cone metric spaces over Banach algebras. Furthermore, some examples are given in order to strengthen our new concepts. Also, based on the powerful notion of a cone metric space over a Banach algebra, we present important applications to systems …
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