Coincidence and common fixed point theorems in Non-Archimedean Menger PM-spaces

• Sunny Chauhan ^[2] ; B. D Pant ^[3] ; Mohammad Imdad ^[1]
  1. [1] Aligarh Muslim University

     Aligarh Muslim University

     India

     
  2. [2] R.H. Government Postgraduate College
  3. [3] Government Degree College

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• Localización: Cubo: A Mathematical Journal, ISSN 0716-7776, ISSN-e 0719-0646, Vol. 15, Nº. 3, 2013, págs. 31-44
• Idioma: inglés
• DOI: 10.4067/S0719-06462013000300004
• Enlaces
  • Texto completo
• Resumen
  • español

    El objetivo de este trabajo es señalar una falacia en la demostración del Teorema 1 contenido en un articulo reciente de Khan et al. [Jordan J. Math. Stat. (JJMS) 5(2) (2012), 137-150] probado en un espacio-PM No-Arquimedeano Menger usando nociones de continuidad subcompatible y sub secuencial. Mostramos que el resultado de Khan et al. [Jordan J. Math. Stat. (JJMS) 5(2) (2012), 137-150] puede recuperarse de dos maneras. Además, establecemos algunos ejemplos ilustrativos que muestran la validez de los resultados principales. Nuestro resultado mejora una gran cantidad de teoremas de punto fijo importantes existentes en la literatura.

  • English

    The object of this work is to point out a fallacy in the proof of Theorem 1 contained in the recent paper of Khan et al. [Jordan J. Math. Stat. (JJMS) 5(2) (2012), 137-150] proved in Non-Archimedean Menger PM-space by using the notions of sub-compatibility and sub-sequential continuity. We show that the results of Khan et al. [Jordan J. Math. Stat. (JJMS) 5(2) (2012), 137-150] an be recovered in two ways. Further, we establish some illustrative examples to show the validity of the main results. Our results improve a multitude of relevant fixed point theorems of the existing literature.

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