The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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𝛿-CONVEX STRUCTURE ON RECTANGULAR METRIC SPACES CONCERNING KANNAN-TYPE CONTRACTION AND REICH-TYPE CONTRACTION

  • Sharma, Dileep Kumar (Department of Mathematics, Government Polytechnic College, Department of Technical Education) ;
  • Tiwari, Jayesh (Department of Computer Science, Shri Vaishnav Institute of Management, Devi Ahilya University)
  • Received : 2022.07.12
  • Accepted : 2022.11.05
  • Published : 2022.11.30
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Abstract

In the present paper, we introduce the notation of 𝛿-convex rectangular metric spaces with the help of convex structure. We investigate fixed point results concerning Kannan-type contraction and Reich-type contraction in such spaces. We also propound an ingenious example in reference of given new notion.

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References

  1. Aron, D., Kumar, S.: Fixed point theorem for a sequence of multivalued nonself mappings in metrically convex metric spaces. Topol. Algebra Appl. 10 (2022), 1-10.
  2. Bakhtin, I. A.: The contraction mapping principle in quasi metric spaces. Functional Anal. Unianowsk Gos. Ped. Inst. 30 (1989), 26-37.
  3. Banach, S.: Surles operations dans les ensembles abstract et leur application aux equation integrals. Fundam Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  4. Beg, I.: An iteration scheme for asymptotically nonexpansive mappings on uniformly convex metric spaces. Nonlinear Anal. Forum 6 (2001), no. 1, 27-34.
  5. Beg, I. & Abbas, M.: Common fixed points and best approximation in convex metric spaces. Soochow J. Math. 33 (2007), no. 4, 729-738.
  6. Beg, I. & Abbas, M.: Fixed point theorem for weakly inward multivalued maps on a convex metric space. Demonstr. Math. 39 (2006), no. 1, 149-160. https://doi.org/10.1515/dema-2006-0119
  7. Branciari, A.: A Fixed point theorem of Banach Caccippoli type on a class of generalised metric spaces. Publ. Math. Debrecen 57 (2000), 31-37. https://doi.org/10.5486/PMD.2000.2133
  8. Chang, S.S., Kim, J.K. & Jin, D.S.: Iterative sequences with errors for asymptotically quasi nonexpansive mappings in convex metric space. Arch. inequal. App. 2 (2004), 365-374.
  9. Czerwik, S.: Contraction mappings in b-metric spaces. Acta. Math. Inform. Univ. Ostraviensis 1 (1993), 5-11.
  10. Ding, XP: Iteration process for nonlinear mappings in convex metric spaces. J. Math. Anal. Appl. 32 (1998), 114-122.
  11. Dragomir, S.S. & Toader, G.H.: Some Inequalities for m-Convex Functions. Studia Univ. Babes-Bolyai, Math. 38 (1993), no. 1, pp. 2128.
  12. Lili Chen, Chaoba Li, Radoslaw Kaczmarek & Yanfeng Zhao: Several fixed point theorems in convex b-metric spaces and applications. MDPI, Mathematics 8 (2020), 242.
  13. Takahashi, W.: Convexity in metric space and nonexpansive mappings. I Kodai Math. Semin. Rep. 32 (1970), 142-149.