In this paper we generalize Hardy–Rogers maps in the context of coupled fixed points. We comment on symmetry some coefficients involved condition, and thus, deduce a simpler formula. generalize, with help obtained main theorem, known results about existence uniqueness market equilibrium duopoly markets. As consequence, ascertain that production should be equal for both participants provided the...

We generalize, extend, and improve some recent fixed point results in conemetric spaces including the results of H. Guang and Z. Xian 2007 ; P. Vetro 2007 ; M. Abbas and G. Jungck 2008 ; Sh. Rezapour and R. Hamlbarani 2008 . In all our results, the normality assumption, which is a characteristic of most of the previous results, is dispensed. Consequently, the results generalize several fixed re...

We survey some classical norm inequalities of Hardy, Kallman, Kato, Kolmogorov, Landau, Littlewood, and Rota the type \[ \|A f\|_{\mathcal{X}}^2 \leq C \|f\|_{\mathcal{X}} \big\|A^2 f\big\|_{\mathcal{X}}, \quad f \in dom\big(A^2\big), \] recall that under exceedingly stronger hypotheses on operator $A$ and/or Banach space $\mathcal{X}$, optimal constant $C$ in these diminishes from $4$ (e.g., w...

*Correspondence: [email protected] 4Department of Mathematics, Kyungnam University Masan, Kyungnam, 631-701, Korea Full list of author information is available at the end of the article Abstract A fixed point theorem is obtained for a monotone self-map in a 0-complete ordered partial metric space under Hardy-Rogers-type contractive condition. This result improves some recently obtained on...

We give an example of an operator that satisfies the curvature condition as defined in [2], but is not similar to the backward shift S ∗ on the Hardy class H. We conclude therefore that the contraction assumption in the similarity characterization given in [2] is a necessary requirement.