* -admissible; α -admissible; Caristi mappings; RC-class and LC-class.">

Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
Volume 12 (2017), 71 -- 80

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.


Arslan Hojat Ansari and Muhammad Usman Ali

Abstract. In this paper, we introduce the notion of (α,ℋLC,fRC)-Caristi type contraction mappings and prove fixed point theorem by using this notion on complete metric space. To illustrate our result, we construct an example.

2010 Mathematics Subject Classification: 47H10; 54H25.
Keywords: α * -admissible; α -admissible; Caristi mappings; RC-class and LC-class.

Full text


  1. M. U. Ali, Fixed point theorem for α -Caristi tpye contraction mappings, J. Adv. Math. Stud., 9 (2016) 1-6. MR3469984. Zbl 1353.54027.

  2. A. H. Ansari, Refinement and generalization of Caristi's fixed point theorem, The 2nd Regional Conference on Mathematics And Applications, PNU, (2014), 382-385.

  3. M. U. Ali and T. Kamran, On (α*,ψ)-contractive multi-valued mappings, Fixed Point Theory Appl., (2013), 2013:137. MR3213155. Zbl 06319488.

  4. M. U. Ali, T. Kamran and E. Karapinar,  A new approach to (α,ψ)-contractive nonself multivalued mappings, J. Inequal. Appl., (2014), 2014:71. MR3345439. Zbl 1338.54151.

  5. M. U. Ali, T. Kamran and Q. Kiran, Fixed point theorem for (α,ψ, φ)-contractive mappings on spaces with two metrics, J. Adv. Math. Stud., 7 (2014), 08-11 MR3287987. Zbl 1329.54040.

  6. M. U. Ali, Q. Kiran and N. Shahzad, Fixed point theorems for multi-valued mappings involving α-function, Abstr. Appl. Anal., 2014 (2014), Article ID 409467. MR3228071.

  7. M. U. Ali, T. Kamran and N. Shahzad:  Best proximity point for α-ψ-proximal contractive multimaps, Abstr. Appl. Anal., 2014 (2014), Article ID 181598. MR3246318.

  8. J. H. Asl, S. Rezapour and N. Shahzad: On fixed points of α-ψ-contractive multifunctions, Fixed Point Theory Appl., (2012), 2012:212. MR3017215. Zbl 1293.54017.

  9. J. Caristi,  Fixed point theorems for mapping satisfying inwardness conditions, Trans. Amer. Math. Soc., 215 (1976), 241-251. MR394329. Zbl 0305.47029.

  10. S. H. Cho, Fixed Point Theorems for α-ψ-Contractive Type Mappings in Metric Spaces, Appl. Math, Sci., 7 (2013), 6765-6778. MR3153155.

  11. E. Karapinar, H. Aydi and B. Samet,  Fixed points for generalized (α,ψ)-contractions on generalized metric spaces, J. Inequal. Appl., (2014), 2014:229. MR3346864.

  12. E. Karapinar, Discussion on (α,ψ) contractions on generalized metric spaces, Abstr. Appl. Anal., 2014 (2014), Article ID 962784. MR3173299.

  13. E. Karapinar and B. Samet, Generalized α-ψ-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012(2012), Article ID 793486. MR2965472. Zbl 1252.54037.

  14. E. Karapinar and R. P. Agarwal, A note on 'Coupled fixed point theorems for α-ψ- contractive-type mappings in partially ordered metric spaces', Fixed Point Theory Appl., (2013), 2013:216. MR3110769. Zbl 1293.54026.

  15. W. A. Kirk, Caristi's fixed point theorem and metric convexity, Collo. Mathe., 36 (1976), 81--86. MR436111. Zbl 0353.53041.

  16. M. A. Kutbi and W. Sintunavarat, On new fixed point results for (α ,ψ ,ξ )-contractive multi-valued mappings on α -complete metric spaces and their consequences, Fixed Point Theory Appl., (2015), 2015:2. MR3359790. Zbl 06582761.

  17. G. Minak and I. Altun, Some new generalizations of Mizoguchi-Takahashi type fixed point theorem, J. Inequal. Appl., (2013), 2013:493. MR3212946. Zbl 1293.54030.

  18. B. Mohammadi, S. Rezapour and N Shahzad, Some results on fixed points of α-ψ-Ciric generalized multifunctions, Fixed Point Theory Appl., (2013), 2013:24. MR3029358. Zbl 06261042.

  19. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α -ψ -contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165. MR2870907. Zbl 1242.54027.

  20. T. Sistani and M. Kazemipour, Fixed point theorems for α-ψ-contractions on metric spaces with a graph, J. Adv. Math. Stud., 7 (2014), 65-79. MR3222294. Zbl 06313110.

Arslan Hojat Ansari
Department of Mathematics
Karaj Branch, Islamic Azad University
Karaj, Iran.

Muhammad Usman Ali
Department of Mathematics
COMSATS Institute of Information Technology
Attock, Pakistan.