Common fixed point theorems for occasionally converse commuting mappings in symmetric spaces

Authors

  • HK Pathak School of Studies in Mathematics, Pt. Ravi Shankar Shukla University, Raipur
  • RK Verma Department of Mathematics, Govt. C. L. C. College Patan, Dist.-Durg

DOI:

https://doi.org/10.3126/kuset.v7i1.5422

Keywords:

commuting mappings, conversely commuting mappings, occasionally converse commuting (occ) mappings, set of commuting mappings, fixed point.

Abstract

In this paper, we introduce the notion of occasionally converse commuting (occ) mappings. Every converse commuting mappings ([1]) are (occ) but the converse need not be true (see, Ex.1.1-1.3). By using this concept, we prove two common fixed point results for a quadruple of self-mappings which satisfy an implicit relation. In first result one pair is (owc) [5] and the other is (occ), while in second result both the pairs are (occ). We illustrate our theorems by suitable examples. Since, there may exist mappings which are (occ) but not conversely commuting, the Theorems 1.1[2], 1.2[2] and 1.3[3] fails to handle those mapping pairs which are only (occ) but not conversely commuting (like Ex.1.4). On the other hand, since every conversely commuting mappings are (occ), so our Theorem 3.1 and 3.2 generalizes these theorems and the main results of Pathak and Verma [6]-[7]  

Mathematics Subject Classifications: 47H10; 54H25.

Keywords and Phrases: commuting mappings; conversely commuting mappings; occasionally converse commuting (occ) mappings; set of commuting mappings; fixed point.

DOI: http://dx.doi.org/ 10.3126/kuset.v7i1.5422

KUSET 2011; 7(1): 56-62  

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How to Cite

Pathak, H., & Verma, R. (2011). Common fixed point theorems for occasionally converse commuting mappings in symmetric spaces. Kathmandu University Journal of Science, Engineering and Technology, 7(1), 56–62. https://doi.org/10.3126/kuset.v7i1.5422

Issue

Vol. 7 No. 1 (2011)

Section

Original Research Articles

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