By employing the generalized Riccati transformation technique, we will establish some new oscillation criteria for a certain class of third order nonlinear delay difference equations. Our results extend and improve some previously obtained ones. An example is worked out to demonstrate the validity of the proposed results.
In this paper, we introduce the concept of α-ψ-ϕ-contractive self mapping in complete ordered partial b-metric space, and we study the existence of fixed points for such mappings under some conditions. Presented theorems in this paper extend and generalize the results derived by Mustafa et al., also some examples are given to illustrate the main results.
Copyright q 2012 Abdelouahed Hamdi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We introduce and consider a proximal point algorithm for solving minimization problems using the… (More)