Ketunggalan Titik Tetap di Ruang Dislocated Quasi B-Metrik pada Pemetaan Siklik
DOI:
https://doi.org/10.15642/mantik.2017.3.1.39-43Keywords:
Dislocated quasi B-Metric space; Cyclic Mapping; Fixed PointAbstract
The quasi b-metric dislocated space (dqb-metric space) was first introduced by Klin-eam and Suanoom in 2015. They had been proven the uniqueness of the fixed point in the dqb-metric space on cyclic mapping that provides the cyclic Banach contraction conditions. Furthermore, in 2016 Dolicanin et al showed that the fixed point singularity properties in the dqb-metric space can be proven without requiring the mapping to satisfy the cyclic metrics Banach contraction conditions. Both statements are proved equivalent in this paper.
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References
[1] Dolic'anin-Dekic', D. T. (2016). A note on recent cyclic fixed point results in dislocated quasi-b-metric spaces. Fixed point theory and applications, 74.
[2] Klin-eam, C, Suanoom, C. (2015). Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions. Fixed point Theory and Applications, 74
[3] Basha, SS, Veeramani, P: Best proximity pair theorems for multifunctions with open fibres. J. Approx. Theory 103, 119-129 (2000)
[4] Enjouji, Y, Nakanishi, M, Suzuki, T: A generalization of Kannan’s fixed point theorem. Fixed Point Theory Appl. 2009, Article ID 192872 (2009)
[5] Kikkawa, M, Suzuki, T: Some similarity between contractions and Kannan mappings. Fixed Point Theory Appl. 2008, Article ID 649749 (2008)
[6] Nakanishi, M, Suzuki, T: An observation on Kannan mappings. Cent. Eur. J. Math. 8, 170-178 (2010)
[7] Reich, S: Kannan’s fixed point theorem. Boll. Unione Mat. Ital. 4, 1-11 (1971)
[8] Shioji, N, Suzuki, T, Takahashi, W: Contractive mappings, Kannan mappings and metric completeness. Proc. Am. Math.Soc. 126, 3117-3124 (1998). doi:10.1090/S0002-9939-98-04605-X
[9] Banach, S: Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundam.Math. 3, 133-181 (1922)
[10] Kannan, R: Some results on fixed points - II. Am. Math. Mon. 76, 405-408 (1969)
[11] Kirk, WA, Srinivasan, PS, Veeramani, P: Fixed points for mapping satisfying cyclic contractive conditions. Fixed Point Theory 4, 79-89 (2003)
[12] Karapinar, E, Erhan, IM: Best proximity on different type contractions. Appl. Math. Inf. Sci. 5, 558-569 (2010)
[13] Wilson, WA: On quasi-metric spaces. Am. J. Math. 53(3), 675-684 (1931)
[14] Hitzler, P, Seda, A: Dislocated topologies. J. Electr. Eng. 51, 3-7 (2000)
[15] Zeyada, FM, Hassan, GH, Ahmad, MA: A generalization of fixed point theorem due to Hitzler and Seda in dislocatedquasi-metric space. Arab. J. Sci. Eng. 31, 111-114 (2005)
[16] Włodarczyk, K, Plebaniak, R, Banach, A: Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces. Nonlinear Anal. 70, 3332-3341 (2009)
[17] Włodarczyk, K, Plebaniak, R, Banach, A: Erratum to: ‘Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces’. Nonlinear Anal. 71, 3585-3586 (2009)
[18] Włodarczyk, K, Plebaniak, R, Obczyłski, C: Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces. Nonlinear Anal. 72, 794-805 (2010)
[19] Włodarczyk, K, Plebaniak, R: Kannan-type contractions and fixed points in uniform spaces. Fixed Point Theory Appl.2011, 90 (2011)
[20] Włodarczyk, K, Plebaniak, R: Contractions of Banach, Tarafdar, Meir-Keller, ´ Ciri´c-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances. J. Math. Anal. Appl. 404, 338-350 (2013)
[21] Włodarczyk, K, Plebaniak, R: Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points. Fixed Point Theory Appl. 2013, 128 (2013)
[22] Włodarczyk, K: Hausdorff quasi-distances, periodic and fixed points for Nadler type set-valued contractions in quasi-gauge spaces. Fixed Point Theory Appl. 2013, 239 (2013)
[23] Włodarczyk, K, Plebaniak, R: Dynamic processes, fixed points, endpoints, asymmetric structures and investigations related to Caristi, Nadler and Banach in uniform spaces. Abstr. Appl. Anal. 2015, Article ID 942814 (2015)
[24] Bakhtin, IA: The contraction principle in quasimetric spaces. In: Functional Analysis, vol. 30, pp. 26-37 (1989)
[25] Czerwik, S: Nonlinear set-valued contraction mappings in b-metric spaces. Atti Semin. Mat. Fis. Univ. Modena 46, 263-276 (1998)
[2] Klin-eam, C, Suanoom, C. (2015). Dislocated quasi-b-metric spaces and fixed point theorems for cyclic contractions. Fixed point Theory and Applications, 74
[3] Basha, SS, Veeramani, P: Best proximity pair theorems for multifunctions with open fibres. J. Approx. Theory 103, 119-129 (2000)
[4] Enjouji, Y, Nakanishi, M, Suzuki, T: A generalization of Kannan’s fixed point theorem. Fixed Point Theory Appl. 2009, Article ID 192872 (2009)
[5] Kikkawa, M, Suzuki, T: Some similarity between contractions and Kannan mappings. Fixed Point Theory Appl. 2008, Article ID 649749 (2008)
[6] Nakanishi, M, Suzuki, T: An observation on Kannan mappings. Cent. Eur. J. Math. 8, 170-178 (2010)
[7] Reich, S: Kannan’s fixed point theorem. Boll. Unione Mat. Ital. 4, 1-11 (1971)
[8] Shioji, N, Suzuki, T, Takahashi, W: Contractive mappings, Kannan mappings and metric completeness. Proc. Am. Math.Soc. 126, 3117-3124 (1998). doi:10.1090/S0002-9939-98-04605-X
[9] Banach, S: Sur les operations dans les ensembles abstraits et leur application aux equations integrales. Fundam.Math. 3, 133-181 (1922)
[10] Kannan, R: Some results on fixed points - II. Am. Math. Mon. 76, 405-408 (1969)
[11] Kirk, WA, Srinivasan, PS, Veeramani, P: Fixed points for mapping satisfying cyclic contractive conditions. Fixed Point Theory 4, 79-89 (2003)
[12] Karapinar, E, Erhan, IM: Best proximity on different type contractions. Appl. Math. Inf. Sci. 5, 558-569 (2010)
[13] Wilson, WA: On quasi-metric spaces. Am. J. Math. 53(3), 675-684 (1931)
[14] Hitzler, P, Seda, A: Dislocated topologies. J. Electr. Eng. 51, 3-7 (2000)
[15] Zeyada, FM, Hassan, GH, Ahmad, MA: A generalization of fixed point theorem due to Hitzler and Seda in dislocatedquasi-metric space. Arab. J. Sci. Eng. 31, 111-114 (2005)
[16] Włodarczyk, K, Plebaniak, R, Banach, A: Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces. Nonlinear Anal. 70, 3332-3341 (2009)
[17] Włodarczyk, K, Plebaniak, R, Banach, A: Erratum to: ‘Best proximity points for cyclic and noncyclic set-valued relatively quasi-asymptotic contractions in uniform spaces’. Nonlinear Anal. 71, 3585-3586 (2009)
[18] Włodarczyk, K, Plebaniak, R, Obczyłski, C: Convergence theorems, best approximation and best proximity for set-valued dynamic systems of relatively quasi-asymptotic contractions in cone uniform spaces. Nonlinear Anal. 72, 794-805 (2010)
[19] Włodarczyk, K, Plebaniak, R: Kannan-type contractions and fixed points in uniform spaces. Fixed Point Theory Appl.2011, 90 (2011)
[20] Włodarczyk, K, Plebaniak, R: Contractions of Banach, Tarafdar, Meir-Keller, ´ Ciri´c-Jachymski-Matkowski and Suzuki types and fixed points in uniform spaces with generalized pseudodistances. J. Math. Anal. Appl. 404, 338-350 (2013)
[21] Włodarczyk, K, Plebaniak, R: Asymmetric structures, discontinuous contractions and iterative approximation of fixed and periodic points. Fixed Point Theory Appl. 2013, 128 (2013)
[22] Włodarczyk, K: Hausdorff quasi-distances, periodic and fixed points for Nadler type set-valued contractions in quasi-gauge spaces. Fixed Point Theory Appl. 2013, 239 (2013)
[23] Włodarczyk, K, Plebaniak, R: Dynamic processes, fixed points, endpoints, asymmetric structures and investigations related to Caristi, Nadler and Banach in uniform spaces. Abstr. Appl. Anal. 2015, Article ID 942814 (2015)
[24] Bakhtin, IA: The contraction principle in quasimetric spaces. In: Functional Analysis, vol. 30, pp. 26-37 (1989)
[25] Czerwik, S: Nonlinear set-valued contraction mappings in b-metric spaces. Atti Semin. Mat. Fis. Univ. Modena 46, 263-276 (1998)
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Published
2017-10-26
How to Cite
malahayati, malahayati. (2017). Ketunggalan Titik Tetap di Ruang Dislocated Quasi B-Metrik pada Pemetaan Siklik. Jurnal Matematika MANTIK, 3(1), 39–43. https://doi.org/10.15642/mantik.2017.3.1.39-43
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