Revisiting Ciric type nonunique fixed point theorems via interpolation

• Autores: Erdal Karapinar
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 22, Nº. 2, 2021, págs. 483-496
• Idioma: inglés
• DOI: 10.4995/agt.2021.16562
• Enlaces
  • Texto completo
• Resumen

  • In this paper, we aim to revisit some non-unique fixed point theorems that were initiated by Ćirić, first.

    We consider also some natural consequences of the obtained results. In addition, we provide a simple example to illustrate the validity of the main result.

• Referencias bibliográficas
  • J. Achari, On Ćirić's non-unique fixed points, Mat. Vesnik 13 (28), no. 3 (1976), 255-257.
  • H. Afshari, H. Aydi and E. Karapinar, On generalized α-ψ-Geraghty contractions on b-metric spaces, Georgian Math. J. 27 (2020), 9-21. https://doi.org/10.1515/gmj-2017-0063
  • H. Afshari, H. Aydi and E. Karapinar, Existence of fixed points of set-valued mappings in b-metric spaces, East Asian Mathematical Journal...
  • R. P. Agarwal and E. Karapinar, Interpolative Rus-Reich-Ciric type contractions via simulation functions, An. St. Univ. Ovidius Constanta,...
  • U. Aksoy, E. Karapinar and I. M. Erhan, Fixed points of generalized alpha-admissible contractions on b-metric spaces with an application to...
  • H. Alsulami, S. Gulyaz, E. Karapinar and I. Erhan, An Ulam stability result on quasi-b-metric-like spaces, Open Mathematics 14, no. 1 (2016),...
  • M. A. Alghamdi, S. Gulyaz-Ozyurt and E. Karapinar, A note on extended Z-contraction, Mathematics 8, no. 2 (2020), 195. https://doi.org/10.3390/math8020195
  • H. Aydi, C.-M. Chen and E. Karapinar, Interpolative Ciric-Reich-Rus type contractions via the Branciari distance, Mathematics 7, no. 1 (2019),...
  • H. Aydi, E. Karapinar and A. F. Roldán López de Hierro, ω-Interpolative Ćirić-Reich-Rus-type contractions, Mathematics 7 (2019), 57. https://doi.org/10.3390/math7010057
  • H. Aydi, M. F. Bota, E. Karapinar and S. Moradi, A common fixed point for weak phi-contractions on b-metric spaces, Fixed Point Theory 13,...
  • H. Aydi, E. Karapinar, M. F. Bota and S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point...
  • V. Berinde, Contracţii Generalizate şi Aplicaţii , Vol. 2, Editura Cub Press, Baie Mare, Romania, 1997.
  • V. Berinde, Sequences of operators and fixed points in quasimetric spaces, Mathematica 41, no. 4 (1996), 23-27.
  • V. Berinde, Generalized contractions in quasi-metric spaces, Seminar on Fixed Point Theory, Babeş-Bolyai University, Research Sem., (1993),...
  • C. Chifu, E. Karapinar and G. Petrusel, Fixed point results in ε-chainable complete b-metric spaces, Fixed Point Theory 21, no. 2 (2020),...
  • L. B. Ćirić, On some maps with a nonunique fixed point, Publ. Inst. Math. 17 (1974), 52-58.
  • S. Czerwik, Contraction mappings in $b$-metric spaces, Acta Math. et Inf. Uni. Ostraviensis 1 (1993), 5-11.
  • A. Fulga, E. Karapinar and G. Petrusel, On hybrid contractions in the context of quasi-metric spaces, Mathematics 8 (2020), 675. https://doi.org/10.3390/math8050675
  • Y. U. Gaba and E. Karapinar, A new approach to the interpolative contractions, Axioms 2019, 8, 110. https://doi.org/10.3390/axioms8040110
  • S. Gulyaz-Ozyurt, On some alpha-admissible contraction mappings on Branciari b-metric spaces, Advances in the Theory of Nonlinear Analysis...
  • S. Gupta and B. Ram, Non-unique fixed point theorems of Ćirić type, (Hindi) Vijnana Parishad Anusandhan Patrika 41, no. 4 (1998), 217-231.
  • R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71-76. https://doi.org/10.2307/2316437
  • E. Karapinar, A new non-unique fixed point theorem, J. Appl. Funct. Anal. 7, no. 1-2 (2012), 92-97. https://doi.org/10.1186/1687-1812-2012-194
  • E. Karapinar, Some nonunique fixed point theorems of Ćirić type on cone metric spaces, Abstr. Appl. Anal. 2010 (2010), Article ID 123094....
  • E. Karapinar, Ciric type nonunique fixed points results: a review, Applied and Computational Mathematics an International Journal 1 (2019),...
  • E. Karapinar, O. Alqahtani and H. Aydi, On interpolative Hardy-Rogers type contractions, Symmetry 11, no. 1 (2019), 8. https://doi.org/10.3390/sym11010008
  • E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl. 2, no. 2 (2018), 85-87. https://doi.org/10.31197/atnaa.431135
  • E. Karapinar, H. Aydi and Z. D. Mitrovic, On interpolative Boyd-Wong and Matkowski type contractions, TWMS J. Pure Appl. Math. 11, no. 2 (2020),...
  • E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics 6, no. 11 (2018),...
  • E. Karapinar, A. Fulga and A. Petrusel, On Istratescu type contractions in $b$-metric spaces, Mathematics 8, no. 3 (2020), 388. https://doi.org/10.3390/math8030388
  • E. Karapinar, A short survey on the recent fixed point results on $b$-metric spaces, Constructive Mathematical Analysis 1, no. 1 (2018), 15-44....
  • E. Karapinar and C. Chifu, Results in wt-distance over $b$-metric spaces, Mathematics 8, no. 2 (2020), 220. https://doi.org/10.3390/math8020220
  • E. Karapinar and A. Fulga, Fixed point on convex $b$-metric space via admissible mappings, TWMS JPAM 12, no. 2 (2021). https://doi.org/10.1155/2021/5538833
  • E. Karapinar, Interpolative Kannan-Meir-Keeler type contraction, Adv. Theory Nonlinear Anal. 5, no. 4 (2021), 611-614. https://doi.org/10.31197/atnaa.989389
  • Z. Liu, Z. Guo, S. M. Kang and S. K. Lee, On Ćirić type mappings with nonunique fixed and periodic points, Int. J. Pure Appl. Math. 26, no....
  • Z. Q. Liu, On Ćirić type mappings with a nonunique coincidence points, Mathematica (Cluj) 35(58), no. 2 (1993), 221-225.
  • B. G. Pachpatte, On Ćirić type maps with a nonunique fixed point, Indian J. Pure Appl. Math. 10, no. 8 (1979), 1039-1043.
  • I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, Romania, 2001.