Volume-3 , Issue-2 , Apr 2016, ISSN 2348-4519 (Online) Go Back

• Open Access   Article

  Weak Compatible and Reciprocally Continuous Maps in Non-Archimedean Menger PM-Space

  Jaya Singh Kushwah

  Research Paper | Isroset-Journal (IJSRMSS)

  Vol.3 , Issue.2 , pp.1-8, Apr-2016

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  Abstract
  In this paper, we introduce weak-compatible maps and reciprocally continuous maps in weak non-Archimedean PM-spaces and establish a common fixed point theorem for such maps. Our result generalizes several fixed point theorems in the sense that all maps involved in the theorem can be discontinuous even at the common fixed point.

  Key-Words / Index Term
  Non-Archimedean Menger probabilistic metric space, Common fixed points, Compatible maps, Weakly Compatible, reciprocally continuous maps

  References
  [1] Cho, Y.J., Ha, K.S. and Chang, S.S., Common fixed point theorems for compatible mappings of type (A) in non-Archimedean Menger PM-spaces, Math. Japonica 48 (1), (1997), 169-179.
  [2] H. K. Pathak, Y. J. Cho, S. S. Chang, S. M. Kang, Compatible mappings of type (P) and fixed point theorems in metric spaces and probabilistic metric spaces, Novi Sad Journal of Mathematics 26 (1996) 87–109.
  [3] Istrătescu, V.I., Fixed point theorems for some classes of contraction mappings on non-archimedean probabilistic metric space, Publ. Math. (Debrecen) 25 (1978), 29-34.
  [4] Istrătescu, V.I. and Crivat, N., On some classes of nonarchimedean Menger spaces, Seminar de spatii Metrices probabiliste, Univ. Timisoara Nr. 12 (1974).
  [5] Jungck, G., Murthy, P.P. and Cho,Y.J., Compatible maps of type (A) and common fixed points, Math. Japon. 38 (1996), 381-390.
  [6] Jain, A. and Singh, B., Common fixed point theorem in Menger space through compatible maps of type (A), Chh. J. Sci. Tech. 2 (2005), 1-12.
  [7] Jain, A. and Singh, B., Common fixed point theorem in Menger Spaces, The Aligarh Bull. of Math. 25 (1), (2006), 23-31..
  [8] Kutukcu, S. and Sharma, S., A Common Fixed Point Theorem in Non-Archimedean Menger PM-Spaces, Demonstratio Mathematica Vol. XLII (4), (2009), 837-849.
  [9] Mishra, S.N., Common fixed points of compatible mappings in PM-spaces, Math. Japon. 36(2), (1991), 283-289.
  [10] Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334.
  [11] Sessa, S., On a weak commutativity condition in fixed point consideration, Publ. Inst. Math. Beograd 32(46), (1982), 146-153.
  [12] Singh, A., Bhatt, S. and Chaukiyal, S., A Unique Common Fixed Point Theorem for Four Maps in Non-Archimedean Menger PM-spaces, Int. Journal of Math. Analysis, Vol. 5, 2011, no. 15, 705 – 712.
  [13] Singh, Bijendra, Jain, Arihant and Agarwal, Pallavi, Common fixed point of coincidentally commuting mappings in non-Archimedean Menger PM-spaces, Italian Journal of Pure and Applied Mathematics 25(2009), 213-218.
  [14] O. Hadzic, A note on I. Istratescu’s xed point theoremin non- Archimedean Menger spaces, Bulletin Mathematique de la Societedes Sciences Mathematiques de Roumanie 24 (1980) 277–280.
  [15] Pant, B.D. and Singh, S.L., Common fixed points of weakly commuting mappings on nonarchimedean Menger spaces, Vikram Math. J., 6 (1986), 27-31.
  

  Citation
  Jaya Singh Kushwah, "Weak Compatible and Reciprocally Continuous Maps in Non-Archimedean Menger PM-Space," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.3, Issue.2, pp.1-8, 2016

• Open Access   Article

  Variable Sampling Plan for Correlated Data

  Mujahida Sayyed

  Review Paper | Isroset-Journal (IJSRMSS)

  Vol.3 , Issue.2 , pp.9-12, Apr-2016

  Abstract

  Full-Text HTML

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  Citation

  Abstract
  In this paper an attempt has been made to study the sampling plan for mean with known CV. The OC of the variable sampling plans for mean with known CV are calculated and compared with the OC of known standard deviation case

  Key-Words / Index Term
  Sampling, Variable, MatLab

  References
  [1] H. Bowker and H. P.Goode (1952): Sampling Inspection by Variables, McGraw-Hill, New York, NY, USA.
  [2] Apley, D. W. and Tsung, F. (2002): The Autoregressive T2 Chart for Monitoring Univariate Auto correlated Processes, Journal of Quality Technology, 34, 80–96.
  [3] D. B. Owen (1996): One-sided variables sampling plans. Industrial Quality Control, vol. 22, 450–4456.
  [4] E. G. Schilling (1982): Acceptance Sampling in Quality Control. Marcel Dekker, New York, NY, USA.
  [5] G. J. Lieberman and G. J. Resnikoff (1955): Sampling plans for inspection by variables. Journal of the American Statistical Association, vol. 50, 457–516.
  [6] Montgomery, D. C. and Mastrangelo, C. M. (1991): Some Statistical Process Control Methods for Auto correlated Data. Journal of Quality Technology, 23, 179–204.
  [7] Narayanan1, G. S. and Rajarathinam, V.(2013). A Procedure for the Selection of Single Sampling Plans by Variables Based on Pareto Distribution. Journal of Quality and Reliability Engineering Volume 2013, Article ID 808741, 5 pages.
  [8] Purkar, Sanjay T. and Khandwawala A.I. (2012): Construction of Operating Characteristics Curve for Acceptance Sampling Plan by Using MATLAB Software. The International Journal of Engineering and Science, Volume 1(1), 44- 48 .
  [9] Sanjay Purkar; A. I. Khandwawala and Govind Maheshwari (2011): Design of a Double Acceptance Sampling Plan to Minimize a Consumer’s Risk Considering an O.C. Curve; A Case Study. International Journal on Emerging Technologies 2(1): 114-118.
  [10] Searls, D.T. (1964): The Utilization of known coefficient of variation in the estimation procedure. Journal of American Statistical association, 59, 1225-1226.
  [11] Vispute, S. and Singh, J. R. (2014): Economic Effect on Variables Sampling Plans Under Second Order Auto-Correlation. International Journal of Scientific Research in Mathematical and Statistical Sciences, vol. 1(2),1-15.
  [12] Zou, C., Wang, Z. and Tsung, F. (2008): Research Monitoring Auto correlated Processes using Variable Sampling Scheme at Fixed-times. Quality Reliability and Engineering International, 24, 55-69.
  

  Citation
  Mujahida Sayyed, "Variable Sampling Plan for Correlated Data," International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.3, Issue.2, pp.9-12, 2016