Zeros of functionals on partial metric spaces with application
Main Article Content
Abstract
We prove a local version of a result obtained recently by Luong anh Hoc on the existence of zeros of functionals on partial metric spaces and apply it to the study of the preservation of zeros of a family of functionals. As a corollary, we derive a preservation result for fixed points of a family of multi-valued mappings in partial metric spaces.
Keywords
Partial metric spaces, fixed points, zeros of functionals
Article Details
References
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[8] S. Han, J. Wu and D. Zhang (2017), Properties and principles on partial metric spaces, Topol. Appl., 230, 77-98.
[9] R. Heckmann (1999), Approximation of metric spaces by partial metric spaces, Appl. Category Struct., 7, 71-83.
[10] N. H. Hoc and L. V. Nguyen (2022), Existence of minima of functions in partial metric spaces and applications to fixed point theory, Acta Math. Hungar., 168, 245-362.
[11] H. P. Kunzi, H. Pajoohesh and M. P. Schellekens (2006), Partial quasi-metrics, Theoret. Comput. Sci., 365, 237-246.
[12] S. G. Matthews (1994), Partial metric topology, in: Papers on General Topology and Applications, (Flushing, NY, 1992), Ann. New York Acad Sci., vol. 728, New York Acad. Sci. (New York), pp. 183-197.
[13] S. Romaguera and O. Valero (2009), A quantitative computational model for complete partial metric spaces via formal balls, Math Struct. Comput. Sci., 19, 541-563.
[14] S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. (2010), Article ID 493298.
[15] M. P. Schellekens (2004), The correspondence between partial metrics and semivaluations, Theoret. Comput. Sci., 315, 135-149.
[16] C. Vetro and P. Vetro (2014), Metric or partial metric spaces endowed with a finite number of graphs: A tool to obtain fixed point results, Topol. Appl., 164, 125-137.
[17] C. Vetro and P. Vetro (2015), A homotopy fixed point theorem in 0-complete partial metric spaces, Filomat, 29, 2037-2048.
[2] T. Abedeljawad, E. Karapinar and K. Tas (2011), Existence and uniqueness of a common fixed point on partial metric spaces, Appl Math Lett., 24, 1894-1899.
[3] M. Abbas, B. Ali and C. Vetro (2013), A Suzuki type fixed point theorem for ag eneralized multivalued mapping on partial Hausdorff metric spaces, Topol. Appl., 160, 553-563.
[4] H. Aydi, M. Abbas and C. Vetro (2012), Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric space, Topol Appl., 159, 3234-3242.
[5] H. Aydi, M. Jellali and E. Karapinar (2015), Common fixed points for generalized α-implicit contractions in partial metric spaces: consequences and application, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Math. RACSAM, 109, 367-384.
[6] I. Beg and H. K. Pathak (2018), A variant of Nadler’s theorem on weak partial metric spaces with application to a homotopy result, Vietnam J. Math., 46, 693-706.
[7] M. A. Cerda-Uguet, M. P. Schellekens and O. Valero (2012), The Baire partial quasi-metric space: a mathematical tool for asymptotic complexity analysis in computer science, Theory Comput. Syst., 50, 387-399.
[8] S. Han, J. Wu and D. Zhang (2017), Properties and principles on partial metric spaces, Topol. Appl., 230, 77-98.
[9] R. Heckmann (1999), Approximation of metric spaces by partial metric spaces, Appl. Category Struct., 7, 71-83.
[10] N. H. Hoc and L. V. Nguyen (2022), Existence of minima of functions in partial metric spaces and applications to fixed point theory, Acta Math. Hungar., 168, 245-362.
[11] H. P. Kunzi, H. Pajoohesh and M. P. Schellekens (2006), Partial quasi-metrics, Theoret. Comput. Sci., 365, 237-246.
[12] S. G. Matthews (1994), Partial metric topology, in: Papers on General Topology and Applications, (Flushing, NY, 1992), Ann. New York Acad Sci., vol. 728, New York Acad. Sci. (New York), pp. 183-197.
[13] S. Romaguera and O. Valero (2009), A quantitative computational model for complete partial metric spaces via formal balls, Math Struct. Comput. Sci., 19, 541-563.
[14] S. Romaguera, A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl. (2010), Article ID 493298.
[15] M. P. Schellekens (2004), The correspondence between partial metrics and semivaluations, Theoret. Comput. Sci., 315, 135-149.
[16] C. Vetro and P. Vetro (2014), Metric or partial metric spaces endowed with a finite number of graphs: A tool to obtain fixed point results, Topol. Appl., 164, 125-137.
[17] C. Vetro and P. Vetro (2015), A homotopy fixed point theorem in 0-complete partial metric spaces, Filomat, 29, 2037-2048.