Fixed point results for generalized cyclic contraction mappings in partial metric spaces

Rus (Approx. Convexity 3:171–178, 2005) introduced the concept of cyclic contraction mapping. P˘acurar and Rus (Nonlinear Anal. 72:1181–1187, 2010) proved some fixed point results for cyclic φ-contraction mappings on a metric space. Karapinar (Appl. Math. Lett. 24:822–825, 2011) obtained a unique fixed point of cyclic weak φ- contraction mappings and studied well-posedness problem for such mappings. On the other hand, Matthews (Ann. New York Acad. Sci. 728:183–197, 1994) introduced the concept of a partial metric as a part of the study of denotational semantics of dataflow networks. He gave a modified version of the Banach contraction principle, more suitable in this context. In this paper, we initiate the study of fixed points of generalized cyclic contraction in the framework of partial metric spaces. We also present some examples to validate our results.S. Romaguera acknowledges the support of the Ministry of Science and Innovation of Spain, grant MTM2009-12872-C02-01.Abbas, M.; Nazir, T.; Romaguera Bonilla, S. (2012). Fixed point results for generalized cyclic contraction mappings in partial metric spaces. Revista- Real Academia de Ciencias Exactas Fisicas Y Naturales Serie a Matematicas. 106(2):287-297. https://doi.org/10.1007/s13398-011-0051-5S2872971062Abdeljawad T., Karapinar E., Tas K.: Existence and uniqueness of a common fixed point on partial metric spaces. Appl. Math. Lett. 24(11), 1894–1899 (2011). doi: 10.1016/j.aml.2011.5.014Altun, I., Erduran A.: Fixed point theorems for monotone mappings on partial metric spaces. Fixed Point Theory Appl. article ID 508730 (2011). doi: 10.1155/2011/508730Altun I., Sadarangani K.: Corrigendum to “Generalized contractions on partial metric spaces” [Topology Appl. 157 (2010), 2778–2785]. Topol. 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Suppression of spatially periodic patterns by dc voltage

The effect of superposed dc and ac applied voltages on two types of spatially periodic instabilities in nematic liquid crystals, flexoelectric domains (FD) and electroconvection (EC), was studied. The onset characteristics, threshold voltages and critical wave vectors, were determined. We found that in general the superposition of driving with different time symmetries inhibits the pattern forming mechanisms for FD and EC as well. As a consequence the onset extends to much higher voltages than the individual dc or ac thresholds. A dc bias induced reduction of the crossover frequency from the conductive to the dielectric EC regimes and a peculiar transition between two types of flexodomains with different wavelengths were detected. Direct measurements of the change of the electrical conductivity and its anisotropy, induced by the applied dc voltage component, showed that the dc bias substantially affects both parameters. Taking into account the experimentally detected variations of the conductivity in the linear stability analysis of the underlying nemato-hydrodynamic equations, a qualitative agreement with the experimental findings on the onset behaviour of spatially periodic instabilities was obtained

Suppression of spatially periodic patterns by dc voltage

The effect of superposed dc and ac applied voltages on two types of spatially periodic instabilities in nematic liquid crystals, flexoelectric domains (FD) and electroconvection (EC), was studied. The onset characteristics, threshold voltages and critical wave vectors, were determined. We found that in general the superposition of driving with different time symmetries inhibits the pattern forming mechanisms for FD and EC as well. As a consequence the onset extends to much higher voltages than the individual dc or ac thresholds. A dc bias induced reduction of the crossover frequency from the conductive to the dielectric EC regimes and a peculiar transition between two types of flexodomains with different wavelengths were detected. Direct measurements of the change of the electrical conductivity and its anisotropy, induced by the applied dc voltage component, showed that the dc bias substantially affects both parameters. Taking into account the experimentally detected variations of the conductivity in the linear stability analysis of the underlying nemato-hydrodynamic equations, a qualitative agreement with the experimental findings on the onset behaviour of spatially periodic instabilities was obtained

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Background To improve continuity of care at hospital admission and discharge and to decrease medication errors pharmaceutical care programs are developed. This study aims to determine the cost-effectiveness of the COACH program in comparison with usual care from a societal perspective. Methods A controlled clinical trial was performed at the Internal Medicine department of a general teaching hospital. All admitted patients using at least one prescription drug were included. The COACH program consisted of medication reconciliation, patient counselling at discharge, and communication to healthcar

Common Fixed Point Results on Generalized Weak Compatible Mapping in Quasi-Partial b-Metric Space

[EN] The focus of this paper is to acquaint with generalized condition (B) in a quasi-partial b-metric space and to establish coincidence and common fixed point theorems for weakly compatible pairs of mapping. Additionally, with the background of quasi-partial b-metric space, the outcomes obtained are exemplified to prove the existence and uniqueness of fixed point.Gautam, P.; Sánchez Ruiz, LM.; Verma, S.; Gupta, G. (2021). Common Fixed Point Results on Generalized Weak Compatible Mapping in Quasi-Partial b-Metric Space. Journal of Mathematics. 2021:1-10. https://doi.org/10.1155/2021/5526801S110202

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