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 [Fuzzy Sets and Systems 27 (1988) 385-389], M. Grabiec in- troduced a notion of completeness for fuzzy metric spaces (in the sense of Kramosil and Michalek) that successfully used to obtain a fuzzy version of Ba- nachs contraction principle. According to the classical case, one can expect that a compact fuzzy metric space be complete in Grabiecs sense. We show here that this is not the case,...

We present sufficient conditions for the existence of solutions of second-order two-point boundary value and fractional order functional differential equation problems in a space where self distance is not necessarily zero. For this, first we introduce a Ciric type generalized F-contraction and F- Suzuki contraction in a metric-like space and give relevance to fixed point results. To illustrate...

Let $mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $mathcal{X}$, where $g$ is a function from $mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in  the unit ball of  the Hilbert space. ...

In this paper, we introduce a pair of generalized proximal contraction mappings and prove the existence of a unique best proximity point for such mappings in a complete metric space. We provide examples to illustrate our result. Our result extends some of the results in the literature.

In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

In this paper, among the other things, we prove the existence and uniqueness theorem of fixed point for mappings on a generalized orthogonal metric space. As a consequence of this, we obtain the existence and uniqueness of fixed point of Cauchy problem for the first order differential equation.

in this paper, we prove the generalized hyers-ulam stability of the quadratic functionalequation$$f(x+y)+f(x-y)=2f(x)+2f(y)$$in non-archimedean $mathcal{l}$-fuzzy normed spaces.