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1
  • COMMON FIXED POINT THEOREMS IN COMPLEX VALUED METRIC SPACE USING IMPLICIT RELATION



Dr.Preeti Sengar

Abstract:
Banach contraction principle in gives appropriate and simple conditions to establish the existence and uniqueness of a solution of an operator equation 𝑇𝑥 = 𝑥. Later, a number of papers were devoted to the improvement and generalization of that result. Most of these results deal with the generalizations of the different contractive conditions in metric spaces. The aim of this paper is to prove the existence and uniqueness of a common fixed point for a pair of mappings satisfying occasionally weakly compatible maps in complex valued metric space using implicit relations.


1-9
2
  • Comparison on Graphite, Graphene Oxide and Reduced Graphene Oxide: Synthesis and Characterization



Ms. Rohini

Abstract:
Graphene oxide (GO) and reduced graphene oxide (RGO) are known to have superior properties for various applications. This work compares the properties of GO and RGO with graphite. GO was prepared by using Improved Hummer’s method whereas the produced GO was subjected to chemical reduction with the use of hydrazine hydrate. Graphite, GO and RGO had different morphologies, quality, functionalized groups, UV-Vis absorption peaks and crystallinity. With the removal of oxygen-containing functional group during reduction for RGO, the quality of samples was decreased due to higher intensity of D band than G band was seen in Raman results. In addition, platelet-like surface can be observed on the surface of graphite as compared to GO and RGO where wrinkled and layered flakes, and crumpled thin sheets were observed on GO and RGO surface respectively. Fourier Transform Infra-Red (FTIR) analysis showed the presence of abundant oxygen-containing functional groups in GO as compared to RGO and graphite. The characteristic peaks at 26.62°, 9.03° and 24.10° for graphite, GO and RGO, respectively, can be detected from X-Ray diffraction (XRD). Furthermore, the reduction also caused red shift at 279nm from 238nm, as obtained from ultraviolet visible (UV-Vis) analysis. The results proved that GO was successfully oxidized from graphite whereas RGO was effectively reduced from GO.


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