DOI QR코드

DOI QR Code

UTILIZING GENERALIZED MEIR-KEELER CONTRACTION IN PERIODIC BOUNDARY VALUE PROBLEMS

  • Handa, Amrish (Department of Mathematics, Govt. P. G. Arts and Science College)
  • 투고 : 2020.08.28
  • 심사 : 2021.09.15
  • 발행 : 2021.11.30

초록

This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.

키워드

참고문헌

  1. S.A. Al-Mezel, H. Alsulami, E. Karapinar & A. Roldan: Discussion on multidimensional coincidence points via recent publications. Abstr. Appl. Anal. Volume 2014, Article ID 287492.
  2. V. Berinde & M. Pecurar: Coupled fixed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces. Fixed Point Theory Appl. 2012, 115.
  3. T.G. Bhaskar & V. Lakshmikantham: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65 (2006), no. 7, 1379-1393. https://doi.org/10.1016/j.na.2005.10.017
  4. B.S. Choudhury & A. Kundu: A coupled coincidence point results in partially ordered metric spaces for compatible mappings. Nonlinear Anal. 73 (2010), 2524-2531. https://doi.org/10.1016/j.na.2010.06.025
  5. B.S. Choudhury, N. Metiya & M. Postolache: A generalized weak contraction principle with applications to coupled coincidence point problems. Fixed Point Theory Appl. 2013, 152.
  6. B. Deshpande & A. Handa: Coincidence point results for weak ψ-φ contraction on partially ordered metric spaces with application. Facta Universitatis Ser. Math. Inform. 30 (2015), no. 5, 623-648.
  7. B. Deshpande & A. Handa: On coincidence point theorem for new contractive condition with application. Facta Universitatis Ser. Math. Inform. 32 (2017), no. 2, 209-229. https://doi.org/10.22190/FUMI1702209D
  8. B. Deshpande, A. Handa & C. Kothari: Coincidence point theorem under Mizoguchi-Takahashi contraction on ordered metric spaces with application. Int. J. Math. Appl. 3 (2015), no. (4-A), 75-94.
  9. B. Deshpande, A. Handa & C. Kothari: Existence of coincidence point under generalized nonlinear contraction on partially ordered metric spaces. J. Korean Soc. Math. Educ. Ser. B: Pure Appl. Math. 23 (2016), no. 1, 35-51.
  10. I.M. Erhan, E. Karapinar, A. Roldan & N. Shahzad: Remarks on coupled coincidence point results for a generalized compatible pair with applications. Fixed Point Theory Appl. 2014, 207.
  11. D. Guo & V. Lakshmikantham: Coupled fixed points of nonlinear operators with applications. Nonlinear Anal. 11 (1987), no. 5, 623-632. https://doi.org/10.1016/0362-546X(87)90077-0
  12. A. Handa, R. Shrivastava & V. K. Sharma: Coincidence point results for contraction mapping principle on partially ordered metric spaces with application to ordinary differential equations. Adalaya Journal 8 (2019), no. 9, 734-754.
  13. G. Jungck: Compatible mappings and common fixed points. Internat. J. Math. & Math. Sci. 9 (1986), no. 4, 771-779. https://doi.org/10.1155/S0161171286000935
  14. G. Jungck & B.E. Rhoades: Fixed point for set-valued functions without continuity. Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.
  15. V. Lakshmikantham & L. Ciric: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70 (2009), no. 12, 4341-4349. https://doi.org/10.1016/j.na.2008.09.020
  16. A. Meir & E. Keeler: A theorem on contraction mappings. J. Math. Anal. Appl. 28 (1969), 326-329. https://doi.org/10.1016/0022-247x(69)90031-6
  17. B. Samet: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces. Nonlinear Anal. 72 (2010), 4508-4517. https://doi.org/10.1016/j.na.2010.02.026
  18. B. Samet, E. Karapinar, H. Aydi & V.C. Rajic: Discussion on some coupled fixed point theorems. Fixed Point Theory Appl. 2013, 50.