Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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COMMON FIXED POINT THEOREMS FOR TWO SELF MAPS SATISFYING ξ-WEAKLY EXPANSIVE MAPPINGS IN DISLOCATED METRIC SPACE

  • Kim, Jong Kyu (Department of Mathematics Education, Kyungnam University) ;
  • Kumar, Manoj (Department of Mathematics, Baba Mastnath University) ;
  • Preeti, Preeti (Department of Mathematics, Baba Mastnath University) ;
  • Poonam, Poonam (Department of Mathematics, Govt. College for Women) ;
  • Lim, Won Hee (Department of Mathematics Education, Kyungnam University)
  • Received : 2021.09.21
  • Accepted : 2021.12.21
  • Published : 2022.06.08
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Abstract

In this article, we shall prove a common fixed point theorem for two weakly compatible self-maps 𝒫 and 𝔔 on a dislocated metric space (M, d*) satisfying the following ξ-weakly expansive condition: d*(𝒫c, 𝒫d) ≥ d* (𝔔c, 𝔔d) + ξ(∧(𝔔c, 𝔔d)), ∀ c, d ∈ M, where $${\wedge}(Qc,\;Qd)=max\{d^*(Qc,\;Qd),\;d^*(Qc,\;\mathcal{P}c),\;d^*(Qd,\;\mathcal{P}d),\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(Qc,\;Qd)},\;\frac{d^*(Qc,\;\mathcal{P}c){\cdot}d^*(Qd,\;\mathcal{P}d)}{1+d^*(\mathcal{P}c,\;\mathcal{P}d)}\}$$. Also, we have proved common fixed point theorems for the above mentioned weakly compatible self-maps along with E.A. property and (CLR) property. An illustrative example is also provided to support our results.

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References

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