Article ID: MTJPAM-D-21-00081

Title: Diagonal M-contractive maps on ordered metric spaces


Montes Taurus J. Pure Appl. Math. / ISSN: 2687-4814

Article ID: MTJPAM-D-21-00081; Volume 4 / Issue 3 / Year 2022 (Special Issue), Pages 152-165

Document Type: Research Paper

Author(s): Mihai Turinici a

aA. Myller Mathematical Seminar, A. I. Cuza University, 700506 Iaşi, Romania

Received: 10 February 2022, Accepted: 11 August 2022, Published: 26 November 2022.

Corresponding Author: Mihai Turinici (Email address: mturi@uaic.ro)

Full Text: PDF


Abstract

A (Matkowski type) functional extension – to the realm of ordered metric spaces – is given for the diagonal fixed point result in Ćirić and Prešić (Acta Math. Univ. Comenian. 76, 143–147, 2007) involving Prešić iterative processes.

Keywords: Ordered metric space, Diagonal fixed point, Prešić iterative process, Admissible function, Matkowski functional contraction

References:
  1. M. Abbas, D. Ilić and T. Nazir, Iterative approximation of fixed points of generalized weak Prešić type k-step iterative methods for a class of operators, Filomat 29, 713–724, 2015.
  2. S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3, 133–181, 1922.
  3. F. E. Browder, On the convergence of successive approximations for nonlinear functional equations, Indag. Math. 30, 27–35, 1968.
  4. Y.-Z. Chen, A Prešić type contractive condition and its applications, Nonlinear Anal. 71, 2012–2017, 2009.
  5. L. B. Ćirić and S. B. Prešić, On Prešić type generalization of the Banach contraction mapping principle, Acta Math. Univ. Comenian. 76, 143–147, 2007.
  6. P. N. Dutta and B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl. 2008, 2008; Article ID: 406368.
  7. R. George and M. S. Khan, On Prešić type extension of Banach contraction principle, Int. J. Math. Anal. (Ruse) 5 (21), 1019–1024, 2011.
  8. A. Gholidahaneh, S. Sedghi and V. Parvaneh, Some fixed point results for Perov-Ćirić-Prešić type F-contractions and applications, J. Funct. Spaces 2020, 2020; Article ID: 1464125.
  9. M. S. Khan, M. Berzig and B. Samet, Some convergence results for iterative sequences of Prešić type and applications, Adv. Difference Equ. 2012, 2012; Article ID: 38.
  10. A. Latif, T. Nazir and M. Abbas, Fixed point results for multivalued Preši‘ c type weakly contractive mappings, Mathematics 7 (7), 2019; Aritcle ID: 601.
  11. J. Matkowski, Integrable solutions of functional equations, Dissertationes Math. 127, Polish Sci. Publ., Warsaw, 1975.
  12. P. P. Murthy, A common fixed point theorem of Prešić type for three maps in fuzzy metric space, Annual Rev. Chaos Th. Bifurcations Dyn. Syst. 4, 30–36, 2013.
  13. H. K. Pathak, R. George, H. A. Nabway, M. S. El-Paoumi and K. P. Reshma, Some generalized fixed point results in a b-metric space and application to matrix equations, Fixed Point Theory Appl. 2015, 2015; Article ID: 101.
  14. M. Păcurar, Approximating common fixed points of Prešić-Kannan type operators by a multi-step iterative method, An. Şt. Univ. “Ovidius” Constanţa Ser. Mat. 17, 153–168, 2009.
  15. M. Păcurar, Fixed points of almost Prešić operators by a k-step iterative method, An. Şt. Univ. “Al. I. Cuza” Iaşi Mat. (N.S.) 57, 199–210, 2011.
  16. S. B. Prešić, Sur une classe d’inéquations aux différences finies et sur la convergence de certaines suites, Publ. Inst. Math. (Beograd) (N.S.) 5 (19), 75–78, 1965.
  17. R. Rajagopalan, A generalised fixed point theorem for set valued Prešić type contractions in a metric space, Internat. J. Engrg. Sci. 13, 3872–3876, 2020.
  18. K. P. R. Rao, M. M. Ali and B. Fisher, Some Prešić type generalizations of the Banach contraction principle, Math. Morav. 15, 41–47, 2011.
  19. I. A. Rus, An iterative method for the solution of the equation x = f(x, …, x), Mathematica (Rev. Anal. Num. Th. Approx.) 10, 95–100, 1981.
  20. I. A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca, 2001.
  21. N. Shahzad and S. Shukla, Set-valued G-Prešić operators on metric spaces endowed with a graph and fixed point theorems, Fixed Point Theory Appl. 2015, 2015; Article ID: 24.
  22. S. Shukla, N. Mlaiki and H. Aydi, On (G,G)-Prešić-Ćirić operators in graphical metric spaces, Mathematics 7, 2019, Article ID: 445.
  23. S. Shukla, S. Radenović and S. Pantelić, Some fixed point theorems for Prešić-Hardy-Rogers type contractions in metric spaces, J. Math. 2013, 2013; Article ID: 295093.
  24. M. R. Tasković, Some results in the fixed point theory, Publ. Inst. Math. (Beograd) (N.S.) 20 (34), 231–242, 1976.
  25. M. R. Tasković, On a question of priority regarding a fixed point theorem in a Cartesian product of metric spaces, Math. Morav. 15, 69–71, 2011.
  26. M. Turinici, Wardowski implicit contractions in metric spaces, 2013; ArXiv: 1211-3164-v2.
  27. M. Turinici, Modern directions in metrical fixed point theory, Pim Editorial House, Iaşi, 2016.
  28. M. Turinici, Reports in metrical fixed point theory, Pim Editorial House, Iaşi, 2020.
  29. S. S. Yeşilkaya, Prešić type operators for a pair mappings, Turk. J. Math. Comput. Sci. 13, 204–210, 2021.