The main purpose of this paper is to obtain sufficient conditions for existence of points of coincidence and common fixed points for a pair of self mappings satisfying some expansive type conditions in $b$-metric spaces. Finally, we investigate that the equivalence of one of these results in the context of cone $b$-metric spaces cannot be obtained by the techniques using scalarization function....

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 de ne a metric on the collection of all translation invarinat spaces on a locally compact abelian group and we study some properties of the metric space.

In this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy M-complete metric spaces. We also give an affirmative partial answer to a question posed by Wardowski [D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Set Syst., {bf 222}(2013), 108-114].Some examples are also g...

in this paper we investigate common xed point theorems for contraction mapping in fuzzy metric space introduced by gregori and sapena [v. gregori, a. sapena, on xed-point the- orems in fuzzy metric spaces, fuzzy sets and systems, 125 (2002), 245-252].

In the present paper, we give a new approach to Caristi's fixed pointtheorem on non-Archimedean fuzzy metric spaces. For this we define anordinary metric $d$ using the non-Archimedean fuzzy metric $M$ on a nonemptyset $X$ and we establish some relationship between $(X,d)$ and $(X,M,ast )$%. Hence, we prove our result by considering the original Caristi's fixedpoint theorem.

We construct one-step iterative process for an α- nonexpansive mapping and a mapping satisfying condition (C) in the framework of a convex metric space. We study △-convergence and strong convergence of the iterative process to the common fixed point of the mappings. Our results are new and are valid in hyperbolic spaces, CAT(0) spaces, Banach spaces and Hilbert spaces, simultaneously.