Fixed point results for set-valued contractions by altering distances in complete metric spaces

Nadler’s contraction principle has led to fixed point theory of set-valued contraction in non-linear analysis. Inspired by the results of Nadler, the fixed point theory of set-valued contraction has been further developed in different directions by many authors, in particular, by Reich, Mizoguchi–Takahashi, Feng–Liu and many others. In the present paper, the concept of generalized contractions for set-valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions. Our first result extends and generalizes the Nadler, Feng–Liu and Klim–Wardowski theorems and the second result is different from the Reich and Mizoguchi–Takahashi results. As a consequence, we derive some results related to fixed point of set-valued maps satisfying certain conditions of integral type.     

Best approximation theorems for nonexpansive and condensing mappings in hyperconvex spaces

In hyperconvex metric spaces we consider best approximation, invariant approximation and best proximity pair problems for multivalued mappings that are condensing or nonexpansive.     

Encapsulation and characterization of flurbiprofen loaded poly(є-caprolactone)–poly(vinylpyrrolidone) blend micropheres by solvent evaporation method

Flurbiprofen loaded PCL/PVP blend microspheres were prepared by o/w solvent evaporation method using various concentrations of gelatin as emulsifying agent. Microsphere recovery decreased with a decrease in the concentration of the emulsifier in the dispersion. Encapsulation efficiency and drug loading of microspheres increased with decrease in concentration of emulsifying agent. Hydration rate, encapsulation efficiency and drug loading of microspheres increased with increase in concentration of PVP. Rheological properties showed free flowing nature of microspheres. SEM (Scanning electron microscope) revealed microspheres were discrete, spherical and became porous with decrease in concentration of emulsifying agent but smooth with higher concentration of emulsifying agent. FTIR (Fourier transform infrared spectroscopy) spectra of pure and encapsulated flurbiprofen in all formulation showed no significant difference in characteristic peaks, suggesting stability of flurbiprofen during encapsulation process. X-RD (X-ray powder diffractometry) of pure flurbiprofen shows sharp peaks, which decreases on encapsulation, indicating dispersion at molecular level and hence decrease in the crystallinity of drug in microspheres. Microspheres showed an enteric nature at pH 1.2 and a sustained release pattern at pH 6.8. Rapid drug release was observed in microspheres with higher concentration of PVP (polyvinylpyrrolidone), PVP acts as channeling agent. Formulation with low concentration of emulsifying agent also showed a fast release due to porous structure. Drug release kinetics followed zero order at pH 1.2 while at pH 6.8 Higuchi model was best fitted and was found non fickian.     

Effect of ion irradiation induced defects on the excess conductivity of Cu1−xTlxBa2Ca1Cu2O8−δ superconductor thin films

The Cu_1?xTl_xBa₂Ca₁Cu₂O_8?δ superconductor thin film samples were bombarded with protons, Si and Au ions of energies 6, 20 and 20 MeV respectively using 5MV tandem pelletron accelerator at Experimental Physics Labs. Each un-irradiated sample had different values of normal state resistivity and the zero resistance critical temperature. The zero resistivity critical temperature has been increased after the irradiation by Si and Au ions. The fluctuation induced conductivity (FIC) analysis of the as-prepared and the ion irradiated samples were performed in the light of Aslamasov–Larkin (AL) theory. The FIC analysis has shown three dimensional (3D) fluctuations in the order parameter in all the samples along with a cross-over to two dimensional (2D) fluctuations at higher temperature. The 3D–2D cross-over temperature has been shifted to higher values after the ion irradiation. Moreover, a direct correlation between the zero resistivity critical temperature, 2D–3D cross-over temperature (T_LD) and superconductivity fluctuation temperature (T_scf) was observed. These studies have shown that the fluctuation induced conductivity (excess conductivity) depends on the density of defects and is independent of their nature.     

Cascade-exciton model analysis of level density parameter dependence in proton induced fission cross sections of some sub-actinide nuclei

Fission cross sections strongly depend on the ratio of the level density parameter in fission to neutron emission, a_f/a_n. In this work, a cascade-exciton model implemented in the code CEM95 has been used to observe this effect for proton induced fission cross sections of tungsten, lead and bismuth. The method was employed using different level density parameter ratios for each fission cross section calculation. The calculated fission cross sections are compared with the available experimental data in the literature. It has been observed that a change of the ratio of the level density parameter, a_f/a_n, is necessary with the incident energy of the proton, to best estimate the fission cross sections in CEM95.     

Landau damping of ion-acoustic waves with simultaneous effects of non-extensivity and non-thermality in the presence of hybrid Cairns-Tsallis distributed electrons

The dispersion properties and Landau damping rate of ion-acoustic waves (IAWs) with the hybrid Cairns-Tsallis distributed (CTD) electrons and Maxwellian ions are investigated using the plasma kinetic model based on Vlasov-Poisson's equations. For both super-extensive (q < 1) and sub-extensive (q > 1) plasmas, the dielectric response function, real frequency, and Landau damping rate of IAWs are derived. By taking the effect of θ_{i, e} (ion-to-electron temperature ratio) into account, it is found that with the increase of ion temperature, the real frequency and wave dispersion effects increase as well (for both super-extensive and sub-extensive cases). Exploring the properties of the Landau damping rate of IAWs with the simultaneous presence of non-thermal parameter α and non-extensive parameter q, a comparison of numerical and analytical results is presented. It is found that in different ranges of θ_{e, i} (electron-to-ion temperature ratio), on decreasing the values of the non-extensive parameter and increasing values of the non-thermal parameter, the weak damping rate is observed (vice versa) in super-extensive or super-thermal plasma, although the trend of the damping rate in sub-thermal plasma is similar (as in the case of super-thermal plasma) but is less weak. It is further revealed that the damping rate of IAWs in thermal plasmas (Maxwellian) is stronger than the damping rate of IAWs in the case of non-thermal plasmas (CTD). The current study is applicable to provide deep insight and further allow the exploration of electrostatic plasma modes in different space and laboratory plasma environments where the hybrid CTD plasma exists.     

Viscosity approximation methods for nonexpansive multimaps in Banach spaces

We prove strong convergence of the viscosity approximation process for nonexpansive nonself multimaps. Furthermore, an explicit iteration process which converges strongly to a fixed point of multimap T is constructed. It is worth mentioning that, unlike other authors, we do not impose the condition ＂Tz = {z}＂ on the map T.