Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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NEW PROOFS OF SOME FIXED POINT THEOREMS FOR MAPPINGS SATISFYING REICH TYPE CONTRACTIONS IN MODULAR METRIC SPACES

  • Godwin Amechi Okeke (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri) ;
  • Daniel Francis (Functional Analysis and Optimization Research Group Laboratory (FANORG), Department of Mathematics, School of Physical Sciences, Federal University of Technology Owerri) ;
  • Jong Kyu Kim (Department of Mathematics Education, Kyungnam University)
  • Received : 2022.05.07
  • Accepted : 2022.10.02
  • Published : 2023.03.03
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Abstract

Our aim in this paper is to give some new proofs to fixed point theorems due to Abdou [1] for mappings satisfying Reich type contractions in modular metric spaces. We removed the restriction that ω satisfies the ∆2-type condition imposed on the results of [1]. Furthermore, Lemma 2.6 of [1] which was crucial in the proofs of the results of [1] is not needed in the proofs of our results. Our method of proof is simpler and interesting.

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Acknowledgement

The authors wish to thank the anonymous referees for their useful comments. This paper was completed while the first author was visiting the Abdus Salam School of Mathematical Sciences (ASSMS), Government College University Lahore, Pakistan as a postdoctoral fellow.

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