Revisiting Ciric type nonunique fixed point theorems via interpolation

Authors

DOI:

https://doi.org/10.4995/agt.2021.16562

Keywords:

abstract metric space, non-unique xed point, self-mappings

Abstract

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.

Downloads

Download data is not yet available.

Author Biography

Erdal Karapinar, Industrial University of Ho Chi Minh City

Faculty of Fundamental Science

References

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 32, no. 3 (2016), 319-332. https://doi.org/10.7858/eamj.2016.024

R. P. Agarwal and E. Karapinar, Interpolative Rus-Reich-Ciric type contractions via simulation functions, An. St. Univ. Ovidius Constanta, Ser. Mat. 27, no. 3 (2019), 137-152. https://doi.org/10.2478/auom-2019-0038

U. Aksoy, E. Karapinar and I. M. Erhan, Fixed points of generalized alpha-admissible contractions on b-metric spaces with an application to boundary value problems, Journal of Nonlinear and Convex Analysis 17, no. 6 (2016), 1095-1108.

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), 1087-1103. https://doi.org/10.1515/math-2016-0097

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), 84. https://doi.org/10.3390/math7010084

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, no. 2 (2012), 337-346. https://doi.org/10.1186/1687-1812-2012-44

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 Theory Appl. 2012, 2012:88. https://doi.org/10.1186/1687-1812-2012-88

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), 3-9.

C. Chifu, E. Karapinar and G. Petrusel, Fixed point results in ε-chainable complete b-metric spaces, Fixed Point Theory 21, no. 2 (2020), 453-464. https://doi.org/10.24193/fpt-ro.2020.2.32

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 and its Applications 1 (2017), 1-13. https://doi.org/10.31197/atnaa.318445

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. https://doi.org/10.1155/2010/123094

E. Karapinar, Ciric type nonunique fixed points results: a review, Applied and Computational Mathematics an International Journal 1 (2019), 3-21.

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), 204-212.

E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics 6, no. 11 (2018), 256. https://doi.org/10.3390/math6110256

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. https://doi.org/10.33205/cma.453034

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. 3 (2006), 399-408.

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.

Downloads

Published

2021-12-09

How to Cite

[1]
E. Karapinar, “Revisiting Ciric type nonunique fixed point theorems via interpolation”, Appl. Gen. Topol., vol. 22, no. 2, pp. 483–496, Dec. 2021.

Issue

Section

Articles