Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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THE REICH TYPE CONTRACTION IN A WEIGHTED bν(α)-METRIC SPACE

  • Received : 2023.05.09
  • Accepted : 2023.07.09
  • Published : 2023.12.15
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Abstract

In this paper, the concept of a weighted bν(α)-metric space is introduced as a generalization of the bν(s)-metric space and ν-metric space. We prove some fixed point results of the Reich-type contraction in the weighted bν(α)-metric space. Furthermore, we generalize Reich's theorem by extending the result to a weighted bν(α)-metric space.

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References

  1. A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debrecen, 57 (2000), 31-37.  https://doi.org/10.5486/PMD.2000.2133
  2. S.S. Dragomir, A new refinement of Jensen's inequality in linear spaces with applications, Math. Comput. Modelling, 52(9-10) (2010), 1497-1505.  https://doi.org/10.1016/j.mcm.2010.05.035
  3. R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71-76. 
  4. B.T. Leyew and O.T. Mewomo, Common fixed point results for generalized orthogonal F-Suzuki contraction for family of multivalued mappings in orthogonal b-metric spaces, Commun. Kor. Math. Soc., 37(4) (2022), 1147-1170. 
  5. A.A. Mebawondu, C. Izuchukwu, G.N. Ogwo and O.T. Mewomo, Existence of solutions for boundary value problems and nonlinear matrix equations via F-contraction mappings in b-metric spaces, Asian-Eur. J. Math., 15(11) (2022), 2250201. 
  6. A.A. Mebawondu and O.T. Mewomo, Some fixed point results for TAC-Suzuki contractive mappings, Commun. Kor. Math. Soc., 34(4) (2019), 1201-1222. 
  7. A.A. Mebawondu and O.T. Mewomo, Suzuki type fixed results in a Gb-metric space, Asian-Eur. J. Math., 14(5) (2021), 2150070. 
  8. O.T. Mewomo, B.T. Leyew and M. Abbas, Fixed point results for generalized multivalued orthogonal α - F-contraction of integral type mappings in orthogonal metric spaces, Topol. Algebra Appl., 10(1) (2022), 113-131.  https://doi.org/10.1515/taa-2022-0118
  9. Z.D. Mitrovic and S. Radenovic, The Banach and Reich contractions in bν(s)-metric spaces, J. Fixed Point Theory Appl., 19 (2017), 3087-3095.  https://doi.org/10.1007/s11784-017-0469-2
  10. J.R. Morales, Generalization of Rakotch's Fixed point theorem, Revista de Math. Teoreay Appl., Enero, 9(1) (2002), 25-33.  https://doi.org/10.15517/rmta.v9i1.207
  11. G. A. Okeke, D. Francis and J. K. Kim, New proofs of some fixed point theorems for mappings satisfying Reich type contractions in modular metric spaces, Nonlinear Funct. Anal. Appl., 28(1)(2023), 1-9.. 
  12. E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc., 13 (1962), 459-465.  https://doi.org/10.1090/S0002-9939-1962-0148046-1
  13. K. P. R. Rao, W. Shatanawi, G. N. V. Kishore, K. Abodayeh and D. Ram Prasad, Existence and Uniqueness of Suzuki type result in Sb-metric spaces with application to integral equations, Nonlinear Funct. Anal. Appl., 23(2)(2018), 225-246. 
  14. S. Reich, Fixed points of contractive functions, Boll. della Unione Mat. Italiana, 5 (1972), 26-42. 
  15. S. Reich, Some remarks concerning contraction mappings, Can. Math. Bull., 14 (1997), 121-124.  https://doi.org/10.4153/CMB-1971-024-9
  16. P. Singh, V. Singh and T. Jele, A new relaxed b-metric type and fixed point results, Aust. J. Math. Anal. Appl., 18(1) (2021), 7-8. 
  17. T. Suzuki, B. Alamri and L.A. Khan, Some notes on fixed point theorems in ν-generalized metric space, Bull. Kyushu Inst. Tech. Pure Appl. Math., 62 (2015), 15-23. 
  18. A.A. Zafar and L. Ali, Generalization of Reich's Fixed point theorem, Int. J. Math. Anal., 3(25) (2009), 1239-1243.