Generalization of Meir-Keeler type fixed point theorems

Authors

  • R. P. Pant
  • Vyomesh Pant
  • V. P. Pandey

DOI:

https://doi.org/10.5556/j.tkjm.35.2004.197

Abstract

The purpose of this paper is two fold. In the following pages we prove common fixed point theorems for four mappings $ A$, $B$, $S$ and $ T $ (say) under the Meir-Keeler type $ (\varepsilon, \delta) $ condition, however, without imposing any additional condition on $delta$ or using a $ \phi $-contractive condition together with. Simultaneously we also show that none of the $ A $, $ B $, $ S $ or $ T $ is continuous at their common fixed point. Thus we not only generalize the Meir-Keeler type and Boyd-Wong type fixed point theorems, but also provide one more answer to the problem (see Rhoades [19]) on the existence of a contractive definition, which is strong enough to generate a fixed point but does not force the map to be continuous at the fixed point.

Author Biographies

R. P. Pant

Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital - 263 002, Inida.

Vyomesh Pant

Department of Mathematics, Kumaon University, D.S.B. Campus, Nainital - 263 002, Inida.

V. P. Pandey

Department of Mathematics, Kumaon University Almora Campus, Almora, Uttaranchal, India.

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Published

2004-09-30

How to Cite

Pant, R. P., Pant, V., & Pandey, V. P. (2004). Generalization of Meir-Keeler type fixed point theorems. Tamkang Journal of Mathematics, 35(3), 179-188. https://doi.org/10.5556/j.tkjm.35.2004.197

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Section

Papers