Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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COMMON FIXED POINT FOR RECIPROCALLY CONTINUOUS AND WEAKLY COMPATIBLE MAPS IN A G-METRIC SPACE

  • Swapna, P. (Department of Mathematics, JNTUH College of Engg. (MVSR Engineering College)) ;
  • Phaneendra, T. (Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology) ;
  • Rajashekar, M.N. (Department of Mathematics, JNTUH College of Engg.)
  • Received : 2021.07.04
  • Accepted : 2022.03.20
  • Published : 2022.09.01
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Abstract

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

Keywords

Acknowledgement

The authors are highly thankful to the referee/referees for their invaluable suggestions in improving the paper.

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