Nonlinear Functional Analysis and Applications

  • 제28권4호
  • /
  • Pages.957-988
  • /
  • 2023
  • /
  • 1229-1595(pISSN)
  • /
  • 2466-0973(eISSN)
경남대학교 수학교육과 (Kyungnam University, Department of Mathematics Eduaction)
권호 표지
DOI QR코드

DOI QR Code

EXISTENCE AND UNIQUENESS OF FIXED POINT OF SOME EXPANSIVE-TYPE MAPPINGS IN GENERALIZED 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)
  • 투고 : 2023.03.03
  • 심사 : 2023.07.29
  • 발행 : 2023.12.15
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

We define new classes of expansive-type mappings in the setting of modular 𝜔G-metric spaces and prove the existence of common unique fixed point for these classes of expansive-type mappings on 𝜔G-complete modular 𝜔G-metric spaces. The results established in this paper extend, improve, generalize and compliment many existing results in literature. We produce some examples to validate our results.

키워드

참고문헌

  1. B. Ahmad, M. Ashraf and B.E. Rhoades, Fixed point theorems for expansive mappings in D-metric spaces, Indian J. Pure Appl. Math., 32 (2001), 1513-1518.
  2. B. Azadifar, M. Maramaei and G. Sadeghi, On the modular G-metric spaces and fixed point theorems, J. Nonlinear. Sci. Appl., 6 (2013), 293-304. https://doi.org/10.22436/jnsa.006.04.07
  3. A. Azizi, R. Moradi and A. Razani, Expansive mappings and their applications in modular space, Abst. Appl. Anal., 2014 (2014) article ID: 580508 8 pages, doi.org/10.1155/2014/580508.
  4. B. Baskaran, C. Rajesh and S. Vijayakumar, Some results in fixed point theorems for expansive mappings in 2-Metric space, Inter. J. Pure Appl. Math., 6(114) (2017), 177-184. https://doi.org/10.11648/j.pamj.20170606.14
  5. R.K. Bisht, M. Jain and S. Kumar, Erratum to: common fixed point theorems for expansion mappings in various spaces, Acta. Math. Hungar., 146 (2015), 261-264. https://doi.org/10.1007/s10474-015-0494-9
  6. V.V. Chistyakov, Metric modular spaces, I basic concepts, Nonlinear Anal. Theory Meth. Appl., 72 (2010), 1-14. https://doi.org/10.1016/j.na.2009.04.057
  7. V.V. Chistyakov, Metric modular spaces, II Applications to superposition operators, Nonlinear Anal., 72 (2010), 15-30. https://doi.org/10.1016/j.na.2009.04.018
  8. V.V. Chistyakov, A fixed point theorem for contractions in metric modular spaces, Functional Analysis, arXiv:1112.5561 (2011), 65-92.
  9. B.C. Dhage, Generalized metric space and mapping with fixed point, Bull. Cal. Math. Soc., 84 (1992), 329-336.
  10. S. Gahler, 2-metrische Raume und ihre topologische struktur, Math. Nacher., 26 (1966), 665-667.
  11. S.M. Kang, S.S. Chang and J.W. Ryu, Common fixed points of expansive mappings, Math. Japonica, 34 (1989), 373-379.
  12. S. Kumar, Common fixed point theorems for expansive mappings in various spaces, Acta. Math. Hungar., 118 (2008), 9-28. https://doi.org/10.1007/s10474-007-6142-2
  13. J. Musielak, Orlicz Spaces and Modular Spaces, Lecture Notes Math., 1034, Springer-verlag, Berlin, 1983.
  14. Z. Mustafa, F. Awawdeh and W. Shatanawi, Fixed point theorem for expansive mappings in G-metric spaces, Int. J. Contemp. Math. Sci., 50(5) (2010), 2463-2472.
  15. Z. Mustafa, M. Khandagji and W. Shatanawi, Fixed point results on complete G-metric spaces, Studia Sci. Math.Hunga., 48(3) (2011), 304-319. https://doi.org/10.1556/sscmath.48.2011.3.1170
  16. Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, Proceeding of the International Conference on Fixed Point Theory and Applications, Valencia Spain, July, (2003), 198-198.
  17. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 2(7) (2006), 289-297.
  18. H. Nakano, Modulared semi-ordered linear spaces, Maruzen. Tokyo, 1, 1950.
  19. G.A. Okeke and D. Francis, Fixed point theorems for Geraghty-type mappings applied to solving nonlinear Volterra-Fredholm integral equations in modular G-metric spaces, Arab J. Math. Sci., 2(27) (2021), 214-234. https://doi.org/10.1108/AJMS-10-2020-0098
  20. G.A. Okeke and D. Francis, Fixed point theorems for asymptotically T-regular mappings in preordered modular G-metric spaces applied to solving nonlinear integral equations, J. Anal., 30(2) (2022), 501-545. https://doi.org/10.1007/s41478-021-00354-1
  21. G.A. Okeke and D. Francis, Some fixed-point theorems for a general class of mappings in modular G-metric spaces, Arab J. Math. Sci., 28(2) (2022), 203-216. https://doi.org/10.1108/AJMS-02-2021-0037
  22. G.A. Okeke and D. Francis, Fixed point theorems for some expansive mappings in modular G-metric spaces, 2023 (2023), submitted.
  23. G.A. Okeke, D. Francis and A. Gibali, On fixed point theorems for a class of α-v-Meir-Keeler-type contraction mapping in modular extended b-metric spaces, J. Anal., 30(3) (2022), 1257-1282. https://doi.org/10.1007/s41478-022-00403-3
  24. G.A. Okeke, D. Francis and M. de la Sen, Some fixed point theorems for mappings satisfying rational inequality in modular metric spaces with applications, Heliyon 6 (2020), e04785, https://doi.org/10.1016/j.heliyon.2020.e04785.
  25. G.A. Okeke, D. Francis, M. de la Sen and M. Abbas, Fixed point theorems in modular G-metric spaces, J. Ineq. Appl., 2021 (2021): 163.
  26. 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.
  27. G.A. Okeke and J.K. Kim, Approximation of common fixed point of three multi-valued ρ-quasi-nonexpansive mappings in modular function spaces, Nonlinear Funct. Anal. Appl., 24(4) (2019), 651-664.
  28. W. Orlicz, Collected Papers, PWN, Warszawa. Vols. I, II, 1988.
  29. F. Ouzine, R. Azennar and D. Mentagui, A fixed point theorem on some multi-valued maps in modular spaces, Nonlinear Funct. Anal. Appl., 27(3) (2022), 641-648.
  30. B.E. Rhoades, An expansive mapping theorem, Jnanabha, 23 (1993), 151-152.
  31. N. Sayyadi, On generalized Banach fixed point theorem, Katsina J. Natural Appl. Sci., 1(5) (2016), 39-43.
  32. B. Singh and S. Jain, Common fixed point theorems for three expansive self-maps in D-metric spaces, Demostratio Math., 3(38) (2005), 703-714. https://doi.org/10.1515/dema-2005-0318
  33. R. Vasuki,Fixed point and fixed point theorems for expansive mappings in Menger spaces, Bull. Cal. Math. Soc., 83 (1991), 565-570.
  34. S.Z. Wang, B.Y. Li, Z.M. Gao and K. Iseki, Some fixed point theorems on expansion mappings, Math. Jpn., 29 (1984), 631-636.