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Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

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Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points

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Karapinar, E.; Romaguera Bonilla, S.; Tirado Peláez, P. (2022). Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points. Demonstratio Mathematica (Online). 55(1):939-951. https://doi.org/10.1515/dema-2022-0177

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Título: Characterizations of quasi-metric and G-metric completeness involving w-distances and fixed points
Autor: Karapinar, Erdal Romaguera Bonilla, Salvador Tirado Peláez, Pedro
Entidad UPV: Universitat Politècnica de València. Escola Tècnica Superior d'Enginyeria Informàtica
Fecha difusión:
Resumen:
[EN] Involving w-distances we prove a fixed point theorem of Caristi-type in the realm of (non -necessarily T-1) quasi-metric spaces. With the help of this result, a characterization of quasi-metric completeness is obtained. ...[+]
Palabras clave: Quasi-metric , Complete , W-distance , Fixed point , G-metric
Derechos de uso: Reconocimiento (by)
Fuente:
Demonstratio Mathematica (Online). (eissn: 2391-4661 )
DOI: 10.1515/dema-2022-0177
Editorial:
De Gruyter Open
Versión del editor: https://doi.org/10.1515/dema-2022-0177
Tipo: Artículo

References

J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Am. Math. Soc. 215 (1976), 241–251.

A. W. Kirk, Caristi’s fixed point theorem and metric convexity, Colloq. Math. 36 (1976), 81–86.

H. K. Pathak, An Introduction to Nonlinear Analysis and Fixed Point Theory, Springer, Singapore, 2018. [+]
J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Am. Math. Soc. 215 (1976), 241–251.

A. W. Kirk, Caristi’s fixed point theorem and metric convexity, Colloq. Math. 36 (1976), 81–86.

H. K. Pathak, An Introduction to Nonlinear Analysis and Fixed Point Theory, Springer, Singapore, 2018.

F. Khojasteh, E. Karapınar, and H. Khandani, Some applications of Caristi’s fixed point theorem in metric spaces, Fixed Point Theory Appl. 2016 (2016), 16.

S. Romaguera and P. Tirado, A characterization of Smyth complete quasi-metric spaces via Caristi’s fixed point theorem, Fixed Point Theory Appl. 2015 (2015), 183.

I. Ekeland, Sur les problèmes variationnels, CR Acad. Sci. Paris 275 (1972), 1057–1059.

I. Ekeland, On the variational principle, J. Math. Anal. Appl. 47 (1974), 324–353.

C. Gutiérrez, G. Kassay, V. Novo, and J. L. Ródenas-Pedregosa, Ekeland variational principles in vector equilibrium problems, SIAM J. Optim. 27 (2017), 2405–2425.

E. Hashemi, R. Saadati, and C. Park, Generalized Ekeland’s variational principle with applications, J. Inequal. Appl. 2019 (2019), 250.

C. L. Zhang and N. J. Huang, On Ekeland’s variational principle for interval-valued functions with applications, Fuzzy Sets Syst. 436 (2022), 152–174.

M. Bota, A. Molnár, and C. Varga, On Ekeland’s variational principle in b-metric spaces, Fixed Point Theory 12 (2011), 21–28.

W. Kirk and N. Shahzad, Fixed Point Theory in Distance Spaces, Springer, Cham, 2014.

N. V. Dung and V. T. L. Hang, On relaxations of contraction constants and Caristi’s theorem in b-metric spaces, J. Fixed Point Theory Appl. 18 (2016), 267–284.

R. Miculescu and A. Mihail, Caristi-Kirk Type and Boyd and Wong-Browder-Matkowski-Rus type fixed point results in b-metric spaces, Filomat. 31 (2017), no., 4331–4340.

E. Karapınar, F. Khojasteh, and Z. D. Mitrović, A proposal for revisiting Banach and Caristi type theorems in b-metric spaces, Mathematics 7 (2019), 308.

S. Romaguera, On the correlation between Banach contraction principle and Caristi’s fixed point theorem in b-metric spaces, Mathematics 10 (2022), 136.

M. Abbas, B. Ali, and S. Romaguera, Multivalued Caristi’s type mappings in fuzzy metric spaces and a characterization of fuzzy metric completeness, Filomat 29 (2015), 1217–1222.

J. R. Jachymski, Caristi’s fixed point theorem and selections of set-valued contractions, J. Math. Anal. Appl. 227 (1998), 55–67.

W. Kirk, Metric fixed point theory: a brief retrospective, Fixed Point Theory Appl. 2015 (2015), 215.

M. A. Khamsi, Introduction to metric fixed point theory, In: Topics in Fixed Point Theory, S. Almezel, Q. H. Ansari, and M. A. Khamsi, Eds., Springer, New York-Heidelberg-Dordrecht-London, 2014, pp. 1–32.

M. A. Khamsi and W. M. Kozlowski, Fixed Point Theory in Modular Function Spaces, Birkhauser, Springer, Basel, Switzerland, 2015.

W. M. Kozlowski, A purely metric proof of Caristi’s fixed point theorem, Bull. Aust. Math. Soc. 95 (2017), 333–337.

O. Kada, T. Suzuki, and W. Tahakaski, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon. 44 (1996), 381–391.

S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. 2010 (2010), Article ID 493298.

W-S. Du, A simple proof of Caristi’s fixed point theorem without using Zorn’s lemma and transfinite induction, Thai J. Math. 14 (2016), 259–264.

E. Karapınar and S. Romaguera, On the weak form of Ekeland’s Variational Principle in quasi-metric spaces, Topol. Appl. 184 (2015), 54–60.

K. Darko, H. Lakzian, and V. Rakočević, Ćirić’s and Fisher’s quasi-contractions in the framework of wt-distance, Rend. Circ. Mat. Palermo, II. Ser (2021). https://doi.org/10.1007/s12215-021-00684-w.

L. B. Ćirić, On Sehgal’s map with a contractive iterate at a point, Publ. Inst. Math. 33 (1983), 59–62.

D. Kocev, E. Karapınar, and V. Rakočević, On quasi-contraction mappings of Ćirić and Fisher type via w-distance, Quaest. Math. 42 (2019), 1–14.

E. Karapınar, Z. D. Mitrović, A. Öztürk, and S. Radenović, On a theorem of Ćirić in b-metric spaces, Rend. Circ. Mat. Palermo Ser. II 70 (2020), 217–225.

J. Marín, S. Romaguera, and P. Tirado, Q-Functions on quasimetric spaces and fixed points for multivalued maps, Fixed Point Theory Appl. 2011, 2011, Article ID 603861.

E. Karapınar, S. Romaguera, and P. Tirado, Contractive multivalued maps in terms of Q-functions on complete quasimetric spaces, Fixed Point Theory Appl. 2014 (2014), 53.

S. Cobzaş, Functional Analysis in Asymmetric Normed Spaces, Birkhaüser/Springer, Basel, Switzerland, 2013.

R. Engelking, General Topology, 2nd Edition, Sigma Series Pure Math., Heldermann Verlag, Berlin, 1989.

A. Mainik and A. Mielke, Existence results for energetic models for rate-independent systems, Calc. Var. 22 (2005), 73–99.

S. G. Matthews, Partial metric topology, In: Proceedings of the 8th Summer Conference on General Topology and Applications, Annals of the New York Academy of Sciences, vol. 728 1994, pp. 183–197.

M. Schellekens, The Smyth completion: A common foundation for denotational semantics and complexity analysis, Electronic Notes Theoret. Comput. Sci. 1 (1995), 535–556.

S. Romaguera and M. Schellekens, Quasi-metric properties of complexity spaces, Topology Appl. 98 (1999), 311–322.

S. Romaguera and O. Valero, Domain theoretic characterisations of quasi-metric completeness in terms of formal balls, Math. Struct. Comput. Sci. 20 (2010), 453–472.

J. Goubault-Larrecq, Non-Hausdorff Topology Non-Hausdorff topology and domain theory, New Mathematical Monographs, vol. 22, Cambridge University Press, Cambridge, 2013.

S. Park, On generalizations of the Ekeland-type variational principles, Nonlinear Anal. 39 (2000), 881–889.

S. Al-Homidan, Q. H. Ansari, and J. C. Yao, Some generalizations of Ekeland-type variational principle with applications to equilibrium problems and fixed point theory Nonlinear Anal. TMA 69 (2008), 126–139.

I. L. Reilly, P. V. Subrahmanyam, and M. K. Vamanamurthy, Cauchy sequences in quasi-pseudo-metric space, Mh. Math. 93 (1982), 127–140.

S. Romaguera and O. Valero, On the structure of the space of complexity partial functions, Int. J. Comput. Math. 85 (2008), 631–640.

S. Romaguera, M. P. Schellekens, and O. Valero, The complexity space of partial functions: a connection between complexity analysis and denotational semantics, Int. J. Comput. Math. 88 (2011), 1819–1829.

S. Cobza̧s, Completeness in quasi-metric spaces and Ekeland variational principle, Topol. Appl. 158 (2011), 1073–1084.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7 (2006), 289–297.

R. P. Agarwal and E. Karapınar, Remarks on some coupled fixed point theorems in G-metric spaces, Fixed Point Theory Appl. 2013 (2013), 2.

R. P. Agarwal, E. Karapınar, D. O’Regan, and A. F. Roldán-López-de-Hierro, Fixed Point Theory in Metric Type Spaces, Springer, Cham Heidelberg New York Dordrecht London, 2015.

R. P. Agarwal, E. Karapınar, and A. F. Roldán-López-de-Hierro, Fixed point theorems in quasimetric spaces and applications to multidimensional fixed points on G-metric spaces, J. Nonlinear Convex Anal. 16 (2015), 1787–1816.

R. P. Agarwal, E. Karapınar, and A. F. Roldán-López-de-Hierro, Last remarks on G-metric spaces and fixed point theorems, RACSAM-Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. 110 (2016), 433–456.

T. V. An, N. V. Dung, and V. T. L. Hang, A new approach to fixed point theorems on G-metric spaces, Topol. Appl. 160 (2013), 1486–1493.

E. Karapınar, A. F. Roldán-López-de-Hierro, and B. Samet, Matkowski theorems in the context of quasi-metric spaces and consequences on G-metric spaces, Analele Stiint. ale Univ. Ovidius Constanta Ser. Mat. 24 (2016), 309–333.

Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl. 2009 (2009), 10.

S. Romaguera and P. Tirado, Fixed point theorems that characterize completeness of G-metric spaces, J. Nonlinear Convex Anal. 23 (2022), 1525–1536.

R. Saadati, S. M. Vaezpour, P. Vetro, and B. E. Rhoades, Fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Model. 52 (2010), 797–801.

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