Two results in metric fixed point theory

We establish two fixed point theorems for certain mappings of contractive type. The first result is concerned with the case where such mappings take a nonempty, closed subset of a complete metric space X into X, and the second with an application of the continuation method to the case where they satisfy the Leray–Schauder boundary condition in Banach spaces.     

Adsorption modeling and mechanistic insight of hazardous chromium on para toluene sulfonic acid immobilized-polyaniline@CNTs nanocomposites

The development of highly efficient adsorbents materials for the purification of wastewater has caught a considerable deal of attention these days. Conducting polymers functionalized adsorbents has become a favorable route for enhancing their adsorption capability due to their ease of synthesis at laboratory scale. In this study, functionalized multiwalled carbon nanotube (CNT)-polyaniline (Pani) composites were fabricated using an oxidation polymerization methodology and later doped with para toluene sulfonic acid (pTSA). The CNTs provided an adequate substrate for the adhesion of Pani as well as a large surface area due to its nano size, and pTSA provided additional functionality for the adsorption of differently charged moieties through strong or weak interactions. The as-synthesized pTSA-Pani@CNT nanocomposite was analyzed by the scanning electron microscopy, transmission electron microscopy for the morphological studies and the structural analysis were done by the X-ray diffraction, and X-ray photoelectron spectroscopy (XPS). The characterization results confirmed that the Pani was adhered to the CNTs as well as its successful functionalization with pTSA. The pTSA-Pani@CNT composite was then applied to the adsorptive removal of hexavalent chromium (Cr(VI)) and the composite showed higher adsorption for Cr(VI) than pTSA-CNT and pTSA-Pani, and the maximum removal level was detected at acidic pH. The analyses of the equilibrium isotherms and adsorption kinetics were performed to elucidate the adsorption mechanism. The XPS analysis indicated that Cr(VI) was strongly bounded to the adsorbent and it further indicated that the amine, imine, and hydroxyl functional groups were involved in the adsorption process. This study presents a new insight for the fabrication of highly functional polymer-carbonaceous nanocomposites for the scavenging of heavy metals from water bodies.