Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

In this paper, we discuss the Banach fixed point theorem conditions on optimal exercise boundary of American put option paying continuously dividend yield, to investigate whether its existence, uniqueness, and convergence are derived. respect, consider integral representation which is extracted as a consequence Feynman-Kac formula. order prove above features, define nonempty closed set in space...

We show that, for a (not necessarily continuous) weakly contractive mean-type mapping $\mathbf{M} \colon I^p\to I^p$ (where $I$ is an interval and $p \in \mathbb{N}$), the functional equation $K \circ \mathbf{M}=K$ has at most one solution in family of continuous means I^p \to I$. Some general approach to latter also given.

We introduce Suzuki type P-contractive mappings by taking into account the concepts of contractive, P-contractive, and contractive mappings. Then, for such on compact metric spaces, we present a fixed point theorem that is more general than well-known Edelstein theorem.

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups which are not necessarily locally connected. These results are local analogues of...

In this paper, the notion of θ*-weak contraction is introduced, which utilized to prove some fixed point results. These results are helpful give a positive response certain open question raised by Kannan and Rhoades on existence contractive definition does not force mapping be continuous at point. Some illustrative examples also given support our As applications result, we investigate uniquenes...

best approximation results provide an approximate solution to the fixed point equation $tx=x$, when the non-self mapping $t$ has no fixed point. in particular, a well-known best approximation theorem, due to fan cite{5}, asserts that if $k$ is a nonempty compact convex subset of a hausdorff locally convex topological vector space $e$ and $t:krightarrow e$ is a continuous mapping, then there exi...

*Correspondence: [email protected] Department of Basic Sciences, Faculty of Engineering, Kyushu Institute of Technology, Tobata, Kitakyushu 804-8550, Japan Abstract We give characterizations of the contractive conditions, by using convergent sequences. Since we use a unified method, we can compare the contractive conditions very easily. We also discuss the contractive conditions of int...