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G. Satyanarayana,G. Nageswara Rao,K. Vijaya Babu,G. V. Santosh Kumar,G. Dinesh Reddy 한국물리학회 2019 THE JOURNAL OF THE KOREAN PHYSICAL SOCIETY Vol.74 No.7
In this work, Ni$_{0.7}$Zn$_{0.2}$Cu$_{0.1}$Fe$_{2-x}$Cr$_x$O$_4$ ($x$ = 0.02, 0.04, 0.06, 0.08 and 0.1) ferrites were synthesized by using the solid state reaction method and how relevant properties of the samples were modified accordingly. The structural, morphological, magnetic and electrical features of the ferrites were evaluated by using X-ray diffraction, scanning electron microscopy, Fourier transmission infrared (FTIR) spectra, vibrating sample magnetometry, electron spin resonance and network analyser. The lattice constant decreases with increasing chromium concentration and the decrease in the lattice constant is attributed to the ionic radius of chromium being smaller than that of iron. The distribution of metal cations in the spinel structure was estimated from the X-ray diffraction data and showed that along with Ni$^{2+}$ ions, most of the Zn$^{2+}$ and the Cu$^{2+}$ ions additionally occupied the octahedral [B] sites. The FTIR spectra revealed two prominent frequency bands in the wave number range 400--600 cm$^{-1}$ which confirm the cubic spinel structure. The magnetic properties, such as the initial permeability, saturation magnetization and coercivity, were investigated at room temperature. The frequency-dependent dielectric constant was observed to decrease with increasing chromium concentration. This behavior was using Koop’s phenomenological theory.
COMMON FIXED POINTS OF TWO PAIRS OF GENERALIZED WEAKLY CONTRACTIVE MAPS
G. V. R. BABU,K. NAGESWARA RAO,G. N. ALEMAYEHU 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.4
We define generalized weakly contractive condition for two pairs of selfmaps and prove the existence of common fixed points of these maps under the assumptions that these two pairs of maps are weakly compatible in a complete metric space. The same is extended to a sequence of selfmaps. Also, we prove the same for four such selfmaps in which one pair is compatible, reciprocal continuous and the other one is weakly compatible.