Some Results of Conditionally Sequential Absorbing and Pseudo Reciprocally Continuous Mappings in Probabilistic 2-Metric Space

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K. Satyanna
V. Srinivas

Abstract

The objective of this paper is to generate two results in probabilistic 2-metric space by using the concepts of conditionally sequential absorbing mappings and pseudo reciprocally continuous mappings. These results stand as generalizations of the theorem proved by V. K. Gupta, Arihant Jain and Rajesh Kumar. Further these two outcomes are justified by supporting examples.

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References

  1. A. Mujahid, B.E. Rhodes, Common fixed point theorems for occasionally weakly compatible mappings satisfying a generalized contractive condition, Math. Commun. 13 (2008), 295-301.
  2. H.M. Abu-Donia, H.A. Atia, O.M.A. Khater, Fixed point theorem by using ψ–contraction and (ψ, φ)–contraction in probabilistic 2–metric spaces, Alexandria Eng. J. 59 (2020), 1239–1242. https://doi.org/10.1016/j.aej.2020.02.009.
  3. H. Bouhadjera, C. Godet-Thobie, Common fixed point theorems for pairs of subcompatible maps, ArXiv:0906.3159 [Math]. (2011). http://arxiv.org/abs/0906.3159.
  4. Fréchet, M. Maurice, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo 22 (1906), 1-72.
  5. S. Gähler, 2-metrische Räume und ihre topologische Struktur, Math. Nachr. 26 (1963), 115–148. https://doi.org/10.1002/mana.19630260109.
  6. I. Golet, Fixed point theorems for multivalued mapping in probabilistic 2-metric Spaces, An. St. Univ. Ovidius Constanta 3 (1995), 44-51.
  7. V.K. Gupta, A. Jain, R. Kumar, Common Fixed Point Theorem in probabilistic 2-Metric space by weak compatibility, Int. J. Theor. Appl. Sci. 11 (2019), 09-12.
  8. S. Jafari, M. Shams, Fixed point theorems for ψ-contraction mappings in probabilistic generalized Menger space, Indian J. Pure Appl. Math. 51 (2020), 519–532. https://doi.org/10.1007/s13226-020-0414-8.
  9. G. Jungck, B. E. Rhodes, Some fixed point theorems for compatible maps, Int. J Math. Math. Sci. 16 (1993), 417-428.
  10. U. Mishra, A.S. Ranadive, D. Gopal, Fixed point theorems via absorbing maps, Thai J. Math. 6 (2012), 49-60.
  11. R.P. Pant, S. Padaliya, Reciprocal continuity and fixed point, Jnanabha 29 (1999), 137-143.
  12. D.K. Patel, P. Kumam, D. Gopal, Some discussion on the existence of common fixed points for a pair of maps, Fixed Point Theory Appl. 2013 (2013), 187. https://doi.org/10.1186/1687-1812-2013-187.
  13. K. Satyanna, V. Srinivas, Fixed point theorem using semi compatible and sub sequentially continuous mappings in Menger space, J. Math. Comput. Sci. 10 (2020), 2503-2515. https://doi.org/10.28919/jmcs/4953.
  14. V. Srinivas, K. Satyanna, Some results by using CLR’s-property in probabilistic 2-metric space, Int. J. Anal. Appl. 19 (2021), 904-914. https://doi.org/10.28924/2291-8639-19-2021-904.