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FIXED POINT THEOREMS IN MENGER SPACE USING THE NOTION OF CLR AND JCLR PROPERTY
Z. K. ANSARI,PAWAN KUMAR,BALBIR SINGH 장전수학회 2021 Proceedings of the Jangjeon mathematical society Vol.24 No.4
Employing the common property (E.A), we prove some common xed point theorems for weakly compatible mappings in Menger space using the notion of CLR and JCLR property. Some results on simi- lar lines satisfying quasi contraction condition. Our results substantially further generalization the corresponding theorems contained in (Imdad et al. [8]).
Seo, H. K.,Ansari, S. A.,Parveen, N.,Qadir, S.,Fouad, H.,Shin, H. S.,Cho, M. H.,Ansari, S. G.,Ansari, Z. A. Chapman and Hall 2017 Journal of materials science Materials in electron Vol. No.
<P>Extensive research have been made in improving the dye sensitized solar cells (DSSC) performance by designing, tailoring and enhancing the photoconversion properties of the matrix. The approaches used are material synthesis, dye permutation combinations, use of natural extracts or using several sensitizers. The polymers are also being explored in this regards in their pristine or composite forms. Therefore, in this study an attempt is made to synthesize a mesoporous polyaniline-titanium dioxide (PANI-TiO2) nanocomposites with one pot synthesis approach at different concentrations of PANI (0.3-0.7 ml). Titanium isopropoxide was used as precursor for TiO2 with aniline and the material was synthesized at ice bath temperature. Morphological observations showed that the composite is a mesoporous material with tubular structure where TiO2 particles are seen entrapped in the polymer matrix and found that intercalation can be tailored with PANI concentration. Structural, functional and optical characterization indicate anatase phase of TiO2, with several functional bands that can help in dye interaction and broad absorption bands within visible region. The photocurrent-voltage response was measured with simulated light and source-meter. It is interesting to note that increasing PANI concentration enhances the mesoporous structure and hence increases the dye loading capacity and photoconductivity of the material. The efficiency increased by about 22 % with addition of 0.5 ml of PANI from 0.3 ml. The proposed study has indicated that such material have the potential to be used for DSSC fabrication with which the device performance can further be increased to a better levels.</P>
Variants of compatible mappings in fuzzy metric spaces
Pawan Kumar,Balbir Singh,Z. K. Ansari 원광대학교 기초자연과학연구소 2018 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.15 No.2
In this paper, we introduce the notions of compatible mappings of type(R), type (K) and type (E) in Fuzzy metric spaces and prove some common fixed point theorems for these mappings.In fact, we call these maps as variants of compatible mappings.