KaydedilenlerDerginizi ekleyin

Dergiler / Constructive Mathematical Analysis / 2026 / Volume: 1 Issue: 1

A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces

Erdal Karapınar(ATILIM UNIVERSITY)
Sayfa
—
Yayın Tarihi
2018-09-15
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

It is also aimed to show that there are still enough rooms for several researchers in this interesting direction and a huge application potential.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:The aim of this short survey is to collect and combine basic notions and results in the fixed point theory in the context of $b$-metric spaces.
📊
Temel Bulgular & Veri:The aim of this short survey is to collect and combine basic notions and results in the fixed point theory in the context of $b$-metric spaces.
💡
Sonuç & Katkı:It is also aimed to show that there are still enough rooms for several researchers in this interesting direction and a huge application potential.
🔬Tür:Uygulamalı Anket & Alan Araştırması
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:$b$-Metric space · Fixed point

Abstract

The aim of this short survey is to collect and combine basic notions and results in the fixed point theory in the context of $b$-metric spaces. It is also aimed to show that there are still enough rooms for several researchers in this interesting direction and a huge application potential.

🔖

Bu Makaleye Atıf Yap

Karapınar, E. (2018). A Short Survey on the Recent Fixed Point Results on $b$-Metric Spaces. Constructive Mathematical Analysis, Volume: 1 Issue: 1. https://doi.org/10.33205/cma.453034

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (87)

  1. H. Afshari, H. Aydi, E.Karapinar, Existence of Fixed Points of Set-Valued Mappings in b-Metric Spaces, East Asian mathematical journal, volume 32, issue 3, 2016, Pages 319 332,
  2. H. Afshari, H. Aydi and E. Karapinar, On generalized alpha-phi-geraghty contractions on b-metricspaces, Georgian Math. Journal,
  3. R. P. Agarwal, H. Alsulami, E.Karapınar and F.Khojasteh, Remarks on some recent fixed point results in quaternion-valued metric spaces, Abstract and Applied Analysis, (2014) Article Id: 171624
  4. 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, (2016). Volume 17,Number 6, 1095-1108
  5. Ali and Kamran, On alpha*-phi-contractive multi-valued mappings, Fixed Point Theory and Appl. 2013 2013:137.
  6. M. U. Ali, T. Kamran, E. Karapinar, On (alpha-phi-xi)-contractive multi-valued mappings, Fixed Point Theory Appl., 2014, 2014:7
  7. H. Alsulami, S.Gulyaz, E. Karapinar, I. Erhan, An Ulam stability result on quasi-b-metric-like spaces, Open Mathematics, Volume 14, Issue 1 (Jan 2016) DOI 10.1515/math-2016-0097,
  8. H. Alsulami, S. Almezel, E. Karapinar, F. Khojasteh, A note on fixed point results in complex valued metric spaces, Journal of Inequalities and Applications, 2015, 2015:33
  9. H. H. Alsulami, E. Karapınar, F. Khojasteh, A. F. Roldán-López-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dynamics in Nature and Society2014, Article ID 269286, 10 pages.
  10. H. H. Alsulami, E. Karapnar, V. Rakocevic Ciric Type Nonunique Fixed Point Theorems onb-Metric Spaces, Filomat 31:11 (2017), 3147-3156
  11. P. Amiri, S. Rezapour, N. Shahzad, Fixed points of generalized alpha-phi-contractions, Revista de laReal Academia de Ciencias Exactas, Fisicas y Naturales Serie A Mate.,
  12. H. Aydi, M-F. Bota, E. Karapınar and S. Mitrovic, A fixed point theorem for set-valued quasi-contractions in b-metric spaces, Fixed Point Theory Appl. 2012, 2012:88.
  13. H. Aydi, M-F. Bota, E. Karapınar and S. Moradi, A common fixed point for weak phi-contractions on b-metric spaces, Fixed Point Theory, 13(2012), No 2, 337-346.
  14. H. Aydi, E. Karapınar, B.Samet, Fixed points for generalized (alpha-phi)-contractions on generalized metric spaces, Journal of Inequalities and Applications 2014, 2014:229
  15. I.A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal., Unianowsk Gos. Ped. Inst. 30(1989), 26-37.
  16. S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math. 3 (1922) 133–181.
  17. V. Berinde, Generalized contractions in quasimetric spaces, Seminar on Fixed Point Theory, Preprint no. 3(1993), 3-9.
  18. V. Berinde, Sequences of operators and fixed points in quasimetric spaces, Stud. Univ. ”Babes-Bolyai”, Math., 16(4)(1996), 23-27.
  19. V. Berinde, Contractii generalizatesi aplicatii, Editura Club Press 22, Baia Mare, 1997.
  20. N. Bilgili, E. Karapınar, A note on “Common fixed points for (alpha-phi,beta)-weakly contractive mappings in generalized metric spaces”, Fixed Point Theory Appl. 2013, 2013:287.
  21. R.M. Bianchini, M. Grandolfi, Transformazioni di tipo contracttivo generalizzato in uno spazio metrico, Atti Acad. Naz. Lincei, VII. Ser., Rend., Cl. Sci. Fis. Mat. Natur. 45 (1968), 212-216.
  22. M. F. Bota-Boriceanu, A. Petru¸ sel, Ulam-Hyers stability for operatorial equations, Analel Univ. Al. I. Cuza, Ia¸ si, 57(2011), 65-74.
  23. M.-F. Bota, E. Karapinar and O. Mlesnite, Ulam-Hyers stability results for fixed point problems via alpha-psi-contractive mapping in b-metric space, Abstract and Applied Analysis, 2013 Article Id: 825293
  24. M. Boriceanu, A. Petru¸ sel, I.A. Rus, Fixed point theorems for some multivalued generalized contractions in b-metric spaces, International Journal of Mathematics and Statistics, 6(2010), 65-76.
  25. M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, IJMM, Vol 4, 3(2009), 285-301.
  26. M. Boriceanu, Fixed point theory for multivalued generalized contraction on a set with two b-metrics, Studia Univ. Babes-Bolyai, Mathematica, 3(2009), 3-14.
  27. M. Bota, Dynamical Aspects in the Theory of Multivalued Operators, Cluj University Press, 2010.
  28. N. Bourbaki, Topologie G´ en´ erale, Herman, Paris, 1974.
  29. J. Brzdek, J. Chudziak, and Z. Pales, A fixed point approach to stability of functional equations, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 17, pp. 6728-6732, 2011.
  30. J. Brzdek and K. Ciepliski, A fixed point approach to the stability of functional equations in non-Archimedean metric spaces, Nonlinear Analysis: Theory, Methods and Applications, vol. 74, no. 18, pp. 6861-6867, 2011.
  31. J. Brzdek and K. Cieplinski, A fixed point theorem and the Hyers-Ulam stability in non-Archimedean spaces, Journal of Mathematical Analysis and Applications, vol. 400, no. 1, pp. 68-75, 2013.
  32. L.B. Ciric, On some maps with a nonunique fixed point. Publ. Inst. Math., 17, 52–58 (1974).
  33. S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1993), 5-11.
  34. S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Univ. Modena, 46(1998), 263-276.
  35. T.Do^ senovic, M. Postolache and S. Radenovic, On multiplicative metric spaces: survey FixedPoint Theory and Applications20162016:92
  36. W.-S. Du, A note on cone metric fixed point theory and its equivalence Nonlinear Analysis72 (2010), no: 5, 2259-2261.
  37. M. Frechet Sur quelques points du calcul fonctionnel, Rendic. Circ. Mat. Palermo 22 (1906)1-74.
  38. S.Gupta and B. Ram, Non-unique fixed point theorems of Ciric type, (Hindi) VijnanaParishad Anusandhan Patrika 41( 4), 217–231(1998).
  39. F. Hausdorff. Mengenle hre. W. de Gruyter & Co., 1927.
  40. J. Hasanzade Asl, Sh. Rezapour and N. Shahzad, On fixed points of alpha-phi- contractivemultifunctions, Fixed Point Theory and Applications, 2012(2012), doi:10.1186/1687-1812-2012-212.
  41. N.Hussain, J.R. Roshan, V. Parvaneh and M.Abbas, Common fixed point results for weakcontractive mappings in ordered b-dislocated metric spaces with applications Journal of In-equalities and Applications (2013) 2013:486
  42. N. Hussain, Z. Kadelburg, S. Radenovi´ c, and F.Al-Solamy, Comparison Functions and FixedPoint Results in Partial Metric Spaces, Abstract and Applied Analysis, vol. 2012, Article ID605781, 15 pages, 2012.
  43. J. Heinonen, Lectures on Analysis on Metric Spaces, Springer Berlin, 2001.
  44. D. H. Hyers, On the stability of the linear functional equation, Proceedings of the NationalAcademy of Sciences of the United States of America, vol. 27, no. 4, pp. 222-224, 1941.
  45. M. Jleli and B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed PointTheory Appl. 2012, 2012:210, 7 pages.
  46. E. Karapinar, H. Piri and H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contrac-tion in Complete b-Metric Spaces,,” Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  47. E. Karapinar, H.Piri and H.H. AlSulami, Fixed Points of Generalized F-Suzuki Type Con-traction in Complete b-Metric Spaces” Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  48. E. Karapinar, A New Non-Unique Fixed Point Theorem, J. Appl. Funct. Anal., 7 (2012),no:1-2, 92-97.
  49. E. Karapinar, Some Nonunique Fixed Point Theorems of Ciric type on Cone Metric Spaces,Abstr. Appl. Anal., vol. 2010, Article ID 123094, 14 pages (2010).
  50. E. Karapinar, H. Piri and H. AlSulami, Fixed Points of Generalized F-Suzuki Type Contrac-tion in Complete b-Metric Spaces, Discrete Dynamics in Nature and Society, 2015 (2015),Article ID 969726, 8 pages
  51. E. Karapınar, P. Kuman, P. Salimi, On alpha-phi-Meri-Keeler contractive mappings, Fixed PointTheory Appl. 2013:94 (2013)
  52. E. Karapınar, H.H. Alsulami and M. Noorwali, Some extensions for Geragthy type contractivemappings Journal of Inequalities and Applications 2015:303 (2015)
  53. E. Karapınar, B.Samet, Generalized alpha-phi-Contractive Type Mappings and Related FixedPoint Theorems with Applications Abstract and Applied Analysis Volume 2012, Article ID793486, 17 pages
  54. E. Karapinar and W.-S. Du, A note on b-cone metric and its related results: Generalizationsor equivalence?, Fixed Point Theory and Applications, (2013), 2013:210
  55. F. Khojasteh, S. Shukla, S. Radenovi´ c, A new approach to the study of fixed point theoremsvia simulation functions, Filomat 29:6 (2015), 1189–1194.
  56. M.A. Kutbi, E. Karapinar, J. Ahmed, A. Azam, Some fixed point results for multi-valuedmappings in b-metric spaces, Journal of Inequalities and Applications 2014, 2014:126
  57. A. Latif, M. E. Gordji, E. Karapınar, W. Sintunavarat, Fixed point results for generalized(alpha-phi)-Meir-Keeler contractive mappings and applications, J. Ineq. Appl. 2014, 2014:68.
  58. V. La Rosa, P. Vetro, Common fixed points for ?-?-?-contractions in generalized metricspaces, Nonlinear Anal. Model. Control 19 (2014), no. 1, 43-54
  59. V. L. Laz^ ar, Ulam-Hyers stability for partial differential inclusions, Electronic Journal ofQualitative Theory of Differential Equations, 21 (2012), 1-19.
  60. Liu, Z. Q.: On Ciric type mappings with a nonunique coincidence points, Mathematica (Cluj)35(58),no. 2, 221–225(1993).
  61. Liu, Z., Guo, Z., Kang, S. M., Lee, S. K.: On Ciric type mappings with nonunique fixed andperiodic points, Int. J. Pure Appl. Math., 26(3),399–408 (2006).
  62. B. Mohammadi, S. Rezapour, N Shahzad, Some results on fixed points of alpha-phi-Ciric general-ized multifunctions. Fixed Point Theory Appl., 2013 2013:24 doi:10.1186/1687-1812-2013-24.
  63. J.J. Nieto, R. Rodr´ıguez-López, Contractive Mapping Theorems in Partially Ordered Setsand Applications to Ordinary Differential Equations, Order. 22 (2005) 223–239.
  64. B. G. Pachpatte, On Ciric type maps with a nonunique fixed point, Indian J. Pure Appl.Math., 10( 8), 1039–1043 (1979).
  65. M. Pacurar, A fixed point result for varphi-contractions on b-metric spaces without the bound-edness assumption, Fasc. Math., 43(2010), 127-137.
  66. T. P. Petru, A. Petrusel and J.-C. Yao, Ulam-Hyers stability for operatorial equations andinclusions via nonself operators, Taiwanese Journal of Mathematics, Vol. 15, No. 5, pp.2195-2212, October 2011.
  67. O. Popescu, Some new fixed point theorems for alpha-Geraghty-contraction type maps in metricspaces, Fixed Point Theory Appl. 2014, 2014:190
  68. A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and someapplications to matrix equations, Proc. Amer. Math. Soc. 132 (2003) 1435–1443.
  69. I. A. Rus, The theory of a metrical fixed point theorem: theoretical and applicative relevances,Fixed Point Theory, 9(2008), No. 2, 541-559.
  70. I. A. Rus, Generalized contractions and applications, Cluj University Press, Cluj-Napoca,2001.
  71. I. A. Rus, Remarks on Ulam stability of the operatorial equations, Fixed Point Theory,10(2009), No. 2, 305-320.
  72. I. A. Rus, A. Petru¸ sel, A. Sˆınt^ am^ arian, Data dependence of the fixed points set of somemultivalued weakly Picard operators, Nonlinear Anal. 52(2003), 1947-1959.
  73. P. Salimi, A. Latif, N. Hussain, Modified alpha-phi-contractive mappings with applications, FixedPoint Theory Appl., 2013 2013:151 doi:10.1186/1687-1812-2013-151.
  74. B. Samet, C. Vetro, P. Vetro, Fixed point theorems for alpha-phi-contractive type mappings, Non-linear Analysis 75 (2012), 2154-2165.
  75. B. Samet, C.Vetro, and F.Vetro, Remarks on G-Metric Spaces, International Journal ofAnalysis, Volume 2013 (2013), Article ID 917158, 6 pages
  76. S. Shukla, Partial b-Metric Spaces and Fixed Point Theorems, Mediterr. J. Math. 11 (2014),703711
  77. S. M. Ulam, Problems in Modern Mathematics, John Wiley and Sons, New York, NY, USA,1964.
  78. A. F. Roldán-López-de-Hierro, E. Karapınar, C. Roldán-López-de-Hierro, J. Mart´ınez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput.Appl. Math. 275 (2015) 345–355.
  79. S. Radenovi´ c, Z. Kadelburg, D. Jandrli´ c and A. Jandrli´ c, Some results on weak contractionmaps, Bulletin of the Iranian Mathematical Society Vol. 38 No. 3 (2012), pp 625-645.
  80. M. Turinici, Abstract comparison principles and multivariable Gronwall-Bellman inequalities,J. Math. Anal. Appl. 117 (1986) 100–127.
  81. H. Afshari, H. Aydi, E.Karapinar, Existence of Fixed Points of Set-Valued Mappings in b-Metric Spaces, East Asian mathematical journal, volume 32, issue 3, 2016, Pages 319 332,
  82. W.-S. Du, A note on cone metric fixed point theory and its equivalence Nonlinear Analysis72 (2010), no: 5, 2259-2261.
  83. F. Hausdorff. Mengenle hre. W. de Gruyter & Co., 1927.
  84. E. Karapinar, A New Non-Unique Fixed Point Theorem, J. Appl. Funct. Anal., 7 (2012),no:1-2, 92-97.
  85. E. Karapinar and W.-S. Du, A note on b-cone metric and its related results: Generalizationsor equivalence?, Fixed Point Theory and Applications, (2013), 2013:210
  86. M.A. Kutbi, E. Karapinar, J. Ahmed, A. Azam, Some fixed point results for multi-valuedmappings in b-metric spaces, Journal of Inequalities and Applications 2014, 2014:126
  87. B. Samet, C.Vetro, and F.Vetro, Remarks on G-Metric Spaces, International Journal ofAnalysis, Volume 2013 (2013), Article ID 917158, 6 pages