Nonlinear Functional Analysis and Applications

  • 제28권4호
  • /
  • Pages.1087-1095
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  • 2023
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  • 1229-1595(pISSN)
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  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
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THE REICH TYPE CONTRACTION IN A WEIGHTED bν(α)-METRIC SPACE

  • Pravin Singh (University of KwaZulu-Natal) ;
  • Shivani Singh (University of South Africa, Department of Decision Sciences) ;
  • Virath Singh (University of KwaZulu-Natal)
  • 투고 : 2023.05.09
  • 심사 : 2023.07.09
  • 발행 : 2023.12.15
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초록

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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참고문헌

  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. 
  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. 
  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. 
  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. 
  10. J.R. Morales, Generalization of Rakotch's Fixed point theorem, Revista de Math. Teoreay Appl., Enero, 9(1) (2002), 25-33. 
  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. 
  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. 
  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.