arXiv subjects
Publications and source records attributed to K. Abodayeh.
In this paper, we give an interesting extension of the partial S-metric space which was introduced [4] to the M_s-metric space. Also, we prove the existence and uniqueness of a fixed point for a self mapping on an Ms-metric space under different contraction principles.
Very recently, Mehadi et al [M. Asadi, E. Karapınar, and P. Salimi, New extension of partial metric spaces with some fixed-point results on $M-$metric spaces] extended the partial metric spaces to the notion of $M-$metric spaces. In this article, we study some relations between partial metric spaces and $M-$metric spaces. Also, we generalize Caristi Kirki's Theorem from partial metric spaces to $M-$metric spaces, where we corrected some gaps in the proof of the main Theorem in E. Karapınar [E. Karapınar, Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011: 4, (2011)]. We close our contribution by introducing some examples to validate and verify our extension results.
In this article we studied the relationship between metric spaces and multiplicative metric spaces. Also, we pointed out some fixed and common fixed point results under some contractive conditions in multiplicative metric spaces can be obtained from the corresponding results in standard metric spaces.
Exact solutions for vibrational levels of diatomic molecules via the Morse potential are obtained by means of the asymptotic iteration method. It is shown that, the numerical results for the energy eigenvalues of $^{7}Li_{2}$ are all in excellent agreement with the ones obtained before. Without any loss of generality, other states and molecules could be treated in a similar way.
The asymptotic iteration method is applied, to calculate the angular spheroidal eigenvalues $λ^{m}_{\ell}(c)$ with arbitrary complex size parameter $c$. It is shown that, the obtained numerical results of $λ^{m}_{\ell}(c)$ are all in excellent agreement with the available published data over the full range of parameter values $\ell$, $m$, and $c$. Some representative values of $λ^{m}_{\ell}(c)$ for large real $c$ are also given.