In this paper, our purpose is to establish a common fixed point result for a pair of self-mappings satisfying some generalized cyclic contraction type conditions involving altering distance and control function with two variables in partial metric spaces. Moreover, we provide an example in support of our main result.
References
[1]
Kirk, W.A., Srinivasan, P.S. and Veeramani, P. (2003) Fixed Points for Mappings Satisfying Cyclical Contractive Conditions. Fixed Point Theory, 4, 79-89.
[2]
Alemayehu, G.N. (2014) Common Fixed Point Theorems for Cocyclic Weak Contractions in Compact Metric Spaces. International Journal of Mathematical, Computational, Statistical, Natural and Physical Engineering, 8, 411-413.
[3]
Agarwal, R.P., Alghamdi, M.A. and Shahzad, N. (2012) Fixed Point Theory for Cyclic Generalized Contractions in Partial Metric Spaces. FixedPointTheoryandApplications, 2012, Article No. 40. https://doi.org/10.1186/1687-1812-2012-40
[4]
Karapınar, E. (2011) Fixed Point Theory for Cyclic Weak φ-Contraction. AppliedMathematicsLetters, 24, 822-825. https://doi.org/10.1016/j.aml.2010.12.016
[5]
Karapınar, E. and Yuce, I.S. (2012) Fixed Point Theory for Cyclic Generalized Weak ϕ‐Contraction on Partial Metric Spaces. AbstractandAppliedAnalysis, 2012, Article ID: 491542. https://doi.org/10.1155/2012/491542
[6]
Karapınar, E., Shobkolaei, N., Sedghi, S. and Vaezpour, M. (2012) A Common Fixed Point Theorem for Cyclic Operators on Partial Metric Spaces. Filomat, 26, 407-414. https://doi.org/10.2298/fil1202407k
[7]
Nashine, H.K. (2012) Cyclic Generalized-Weakly Contractive Mappings and Fixed Point Results with Applications to Integral Equations. NonlinearAnalysis: Theory, Methods&Applications, 75, 6160-6169. https://doi.org/10.1016/j.na.2012.06.021
[8]
Păcurar, M. and Rus, I.A. (2010) Fixed Point Theory for Cyclic-Contractions. NonlinearAnalysis: Theory, Methods&Applications, 72, 1181-1187. https://doi.org/10.1016/j.na.2009.08.002
[9]
Sharbu, B., Geremew, A. and Berhane, A. (2017) A Common Fixed Point Theorem for Reich Type Co-Cyclic Contraction in Dislocated Quasi-Metric Paces. EthiopianJournalofScienceandTechnology, 10, 81-94. https://doi.org/10.4314/ejst.v10i2.1
Abdeljawad, T. (2011) Fixed Points for Generalized Weakly Contractive Mappings in Partial Metric Spaces. MathematicalandComputerModelling, 54, 2923-2927. https://doi.org/10.1016/j.mcm.2011.07.013
[12]
Altun, I. and Acar, Ö. (2012) Fixed Point Theorems for Weak Contractions in the Sense of Berinde on Partial Metric Spaces. TopologyandItsApplications, 159, 2642-2648. https://doi.org/10.1016/j.topol.2012.04.004
[13]
Babu, G.V.R. and Ratna Babu, D. (2019) Common Fixed Points of Rational Type and Geraghty-Suzuki Type Contraction Maps in Partial Metric Spaces. Journal of the International Mathematical Virtual Institute, 9, 341-359.
[14]
Bari, C.D. and Vetro, P. (2011) Fixed Points for Weak ψ-Contractions on Partial Metric Spaces. International Journal of Contemporary Mathematical Sciences, 6, 5-12.
[15]
Bukatin, M., Kopperman, R., Matthews, S. and Pajoohesh, H. (2009) Partial Metric Spaces. AmericanMathematicalMonthly, 116, 708-718. https://doi.org/10.4169/193009709x460831
[16]
Ćirić, L., Samet, B., Aydi, H. and Vetro, C. (2011) Common Fixed Points of Generalized Contractions on Partial Metric Spaces and an Application. AppliedMathematicsandComputation, 218, 2398-2406. https://doi.org/10.1016/j.amc.2011.07.005
[17]
Dwivedi, P.K. (2022) Common Fixed Point Theorem on Partial Metric Space. InternationalJournalofMathematicsTrendsandTechnology, 68, 30-37. https://doi.org/10.14445/22315373/ijmtt-v68i4p506
[18]
Gangopadhyay, M., Saha, M. and Baisnab, A.P. (2013) Some Fixed Point Theorem in Partial Metric Spaces. TWMS Journal of Applied and Engineering Mathematics, 3, 206-213.
[19]
Heckmann, R. (1999) Approximation of Metric Spaces by Partial Metric Spaces. AppliedCategoricalStructures, 7, 71-83. https://doi.org/10.1023/a:1008684018933
[20]
Jungck, G. (1996) Common Fixed Points for Noncontinuous Non-Self Maps on Non-Metric Spaces. Far East Journal of Mathematical Sciences, 4, 199-215.
[21]
Karapinar, E. (2011) Generalizations of Caristi Kirk’s Theorem on Partial Metric Spaces. Fixed Point Theory and Applications, 2011, Article No. 4. https://doi.org/10.1186/1687-1812-2011-4
[22]
Karapınar, E. and Erhan, İ.M. (2011) Fixed Point Theorems for Operators on Partial Metric Spaces. AppliedMathematicsLetters, 24, 1894-1899. https://doi.org/10.1016/j.aml.2011.05.013
[23]
Oltra, S. and Valero, O. (2004) Banach’s Fixed Point Theorem for Partial Metric Spaces. Rendicontidell’Istituto di Matematicadell’Università di Trieste, 36, 17-26.
[24]
Romaguera, S. (2009) A Kirk Type Characterization of Completeness for Partial Metric Spaces. FixedPointTheoryandApplications, 2010, Article ID 493298. https://doi.org/10.1155/2010/493298
[25]
Valero, O. (2005) On Banach Fixed Point Theorems for Partial Metric Spaces. AppliedGeneralTopology, 6, 229-240. https://doi.org/10.4995/agt.2005.1957
[26]
Karapinar, E. (2012) Weak ψ-Contraction on Partial Metric Spaces. Journal of Computational Analysis and Applications, 14, 206-210.
[27]
Karapınar, E. and Yüksel, U. (2011) Some Common Fixed Point Theorems in Partial Metric Spaces. JournalofAppliedMathematics, 2011, Article ID 263621. https://doi.org/10.1155/2011/263621
[28]
Karapinar, E. (2011) A Note on Common Fixed Point Theorems in Partial Metric Spaces. MiskolcMathematicalNotes, 12, 185-191. https://doi.org/10.18514/mmn.2011.335
[29]
Mohanta, S.K. and Biswas, P. (2021) Generalized Cyclic Contractions and Coincidence Points Involving a Control Function on Partial Metric Spaces. Journal of Non-linear Analysis and Optimization, 12, 61-81.
[30]
Nashine, H.K. and Karapinar, E. (2013) Fixed Point Results in Orbitally Complete Partial Metric Spaces. Bulletin of the Malaysian Mathematical Sciences Society, 36, 1185-1193.
[31]
Romaguera, S. (2012) Fixed Point Theorems for Generalized Contractions on Partial Metric Spaces. TopologyanditsApplications, 159, 194-199. https://doi.org/10.1016/j.topol.2011.08.026
[32]
Khan, M.S., Swaleh, M. and Sessa, S. (1984) Fixed Point Theorems by Altering Distances between the Points. BulletinoftheAustralianMathematicalSociety, 30, 1-9. https://doi.org/10.1017/s0004972700001659
[33]
Ahmad, A.G.B., Fadail, Z.M., Nashine, H.K., Kadelburg, Z. and Radenović, S. (2012) Some New Common Fixed Point Results through Generalized Altering Distances on Partial Metric Spaces. FixedPointTheoryandApplications, 2012, Article No. 120. https://doi.org/10.1186/1687-1812-2012-120
[34]
Aydi, H. (2013) A Common Fixed Point Result by Altering Distances Involving a Contractive Condition of Integral Type in Partial Metric Spaces. DemonstratioMathematica, 46, 383-394. https://doi.org/10.1515/dema-2013-0450
[35]
Choudhury, B.S. (1970) Unique Fixed Point Theorem for Weakly C-Contractive Mappings. KathmanduUniversityJournalofScience, EngineeringandTechnology, 5, 6-13. https://doi.org/10.3126/kuset.v5i1.2842
[36]
Sastry, K.P.R., Naidu, S.V.R., Babu, G.V.R. and Naidu, G.A. (2000) Generalization of Common Fixed Point Theorems for Weakly Commuting Maps by Altering Distances. TamkangJournalofMathematics, 31, 243-250. https://doi.org/10.5556/j.tkjm.31.2000.399
[37]
Shatanawi, W. and Postolache, M. (2010) Common Fixed Point Results for Mappings under Nonlinear Contraction of Cyclic form in Ordered Metric Spaces. Fixed Point Theory and Applications, 2010, Article ID: 493298.
[38]
Abbas, M., Nazir, T. and Romaguera, S. (2011) Fixed Point Results for Generalized Cyclic Contraction Mappings in Partial Metric Spaces. RevistadelaRealAcademiadeCienciasExactas, FisicasyNaturales.SerieA. Matematicas, 106, 287-297. https://doi.org/10.1007/s13398-011-0051-5
[39]
Altun, I., Sola, F. and Simsek, H. (2010) Generalized Contractions on Partial Metric Spaces. TopologyanditsApplications, 157, 2778-2785. https://doi.org/10.1016/j.topol.2010.08.017
[40]
Haghi, R.H., Rezapour, S. and Shahzad, N. (2011) Some Fixed Point Generalizations Are Not Real Generalizations. NonlinearAnalysis: Theory, Methods&Applications, 74, 1799-1803. https://doi.org/10.1016/j.na.2010.10.052
[41]
Haghi, R.H., Rezapour, S. and Shahzad, N. (2013) Be Careful on Partial Metric Fixed Point Results. TopologyanditsApplications, 160, 450-454. https://doi.org/10.1016/j.topol.2012.11.004
[42]
He, F. and Chen, A. (2016) Fixed Points for Cyclic φ-Contractions in Generalized Metric Spaces. FixedPointTheoryandApplications, 2016, Article No. 67. https://doi.org/10.1186/s13663-016-0558-8
[43]
Karapinar, E. and Nashine, H.K. (2013) Fixed Point Theorems for Kanaan Type Cyclic Weakly Contractions. Nonlinear Analysis and Optimization, 4, 29-35.
[44]
Mohanta, S.K. (2011) A Fixed Point Theorem via Generalized W-Distance. Bulletin of Mathematical Analysis and Applications, 3, 134-139.
[45]
Mohanta, S.K. and Mohanta, S. (2012) A Common Fixed Point Theorem in G-Metric Spaces. Cubo (Temuco), 14, 85-101. https://doi.org/10.4067/s0719-06462012000300006
[46]
Mohanta, S.K. and Patra, S. (2017) Coincidence Points and Common Fixed Points for Hybrid Pair of Mappings in b-Metric Spaces Endowed with a Graph. Journal of Linear and Topological Algebra, 6, 301-321.
[47]
Nashine, H.K. and Kadelburg, Z. (2013) Cyclic Contractions and Fixed Point Results via Control Functions on Partial Metric Spaces. InternationalJournalofAnalysis, 2013, Article ID: 726387. https://doi.org/10.1155/2013/726387
[48]
Yamaod, O., Sintunavarat, W. and Cho, Y.J. (2015) Common Fixed Point Theorems for Generalized Cyclic Contraction Pairs in B-Metric Spaces with Applications. FixedPointTheoryandApplications, 2015, Article No. 164. https://doi.org/10.1186/s13663-015-0409-z
[49]
Abdeljawad, T., Karapınar, E. and Taş, K. (2011) Existence and Uniqueness of a Common Fixed Point on Partial Metric Spaces. AppliedMathematicsLetters, 24, 1900-1904. https://doi.org/10.1016/j.aml.2011.05.014
[50]
Abbas, M. and Jungck, G. (2008) Common Fixed Point Results for Noncommuting Mappings without Continuity in Cone Metric Spaces. JournalofMathematicalAnalysisandApplications, 341, 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070
[51]
Babu, G.V.R. and Alemayehu, G.N. (2010) Point of Coincidence and Common Fixed Points of a Pair of Generalized Weakly Contractive Maps. JournalofAdvancedResearchinPureMathematics, 2, 89-106. https://doi.org/10.5373/jarpm.338.010810