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Approximation of common fixed points in 2-Banach spaces with applications

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Approximation of common fixed points in 2-Banach spaces with applications

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dc.contributor.author Kumar, D. Ramesh es_ES
dc.contributor.author Pitchaimani, M. es_ES
dc.date.accessioned 2019-04-04T07:01:01Z
dc.date.available 2019-04-04T07:01:01Z
dc.date.issued 2019-04-01
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/118957
dc.description.abstract [EN] The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying generalized rational contractive condition in 2-Banach spaces. An example is included to justify our results. We approximate the common fixed point by Mann and Picard type iteration schemes. Further, an application to well-posedness of the common fixed point problem is given. The presented results generalize many known results on 2-Banach spaces. es_ES
dc.description.sponsorship The authors thank the reviewers for valuable comments. The first author D. Ramesh Kumar would like to thank the University Grants Commission, New Delhi, India for providing the financial support in preparation of this manuscript. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València
dc.relation.ispartof Applied General Topology
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Common fixed point es_ES
dc.subject Mann iteration es_ES
dc.subject Picard iteration es_ES
dc.subject Well-posedness es_ES
dc.subject 2-Banach space es_ES
dc.title Approximation of common fixed points in 2-Banach spaces with applications es_ES
dc.type Artículo es_ES
dc.date.updated 2019-04-04T06:29:59Z
dc.identifier.doi 10.4995/agt.2019.9168
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Kumar, DR.; Pitchaimani, M. (2019). Approximation of common fixed points in 2-Banach spaces with applications. Applied General Topology. 20(1):43-55. https://doi.org/10.4995/agt.2019.9168 es_ES
dc.description.accrualMethod SWORD es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2019.9168 es_ES
dc.description.upvformatpinicio 43 es_ES
dc.description.upvformatpfin 55 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 20
dc.description.issue 1
dc.identifier.eissn 1989-4147
dc.contributor.funder University Grants Commission, India
dc.description.references M. Abbas, B. E. Rhoades and T. Nazir, Common fixed points for four maps in cone metric spaces, Applied Mathematics and Computation 216 (2010), 80-86. https://doi.org/10.1016/j.amc.2010.01.003 es_ES
dc.description.references M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008), 416-420. https://doi.org/10.1016/j.jmaa.2007.09.070 es_ES
dc.description.references M. Arshad, E. Karapinar and J. Ahmad, Some unique fixed point theorems for rational contractions in partially ordered metric spaces, J. Inequal. Appl. 2013 es_ES
dc.description.references (1) (2013), 1-16. https://doi.org/10.1186/1029-242x-2013-248 es_ES
dc.description.references A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and optimization 32, no. 3 (2011), 243-253. https://doi.org/10.1080/01630563.2011.533046 es_ES
dc.description.references S. Banach, Sur les opérations dans les ensembles abstraits et leur application auxéquations intégrales, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181 es_ES
dc.description.references I. Beg and A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal. 71, no.9 (2009), 3699-3704. https://doi.org/10.1016/j.na.2009.02.027 es_ES
dc.description.references K. Cieplinski, Approximate multi-additive mappings in 2-Banach spaces, Bull. Iranian Math. Soc. 41, no. 3 (2015), 785-792. es_ES
dc.description.references B. K. Dass and S. Gupta, An extension of Banach's contraction principle through rational expression, Indian J. Pure appl. Math. 6, no. 4 (1975), 1445-1458. es_ES
dc.description.references F. S. De Blasi and J. Myjak, Sur la porosité de l'ensemble des contractions sans point fixe, C. R. Acad. Sci. Paris 308 (1989), 51-54. es_ES
dc.description.references S. Gähler, 2-metrische Räume and ihre topologische strucktur, Math. Nachr. 26 (1963), 115-148. https://doi.org/10.1002/mana.19630260109 es_ES
dc.description.references S. Gähler, Uber die unifromisieberkeit 2-metrischer Räume, Math. Nachr. 28 (1965), 235-244. https://doi.org/10.1002/mana.19640280309 es_ES
dc.description.references S. Gähler, Über 2-Banach-Räume, Math. Nachr. 42 (1969), 335-347. https://doi.org/10.1002/mana.19690420414 es_ES
dc.description.references L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332, no. 2 (2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087 es_ES
dc.description.references W. A. Kirk and N. Shahzad, Some fixed point results in ultrametric spaces, Topology and its Applications 159 (2012), 3327-3334. https://doi.org/10.1016/j.topol.2012.07.016 es_ES
dc.description.references K. Iseki, Fixed point theorems in 2-metric space, Math.Seminar. Notes, Kobe Univ. 3(1975), 133-136. es_ES
dc.description.references E. Matouskova, S. Reich and A. J. Zaslavski, Genericity in nonexpansive mapping theory, Advanced Courses of Mathematical Analysis I, World Scientific Hackensack (2004), 81-98. https://doi.org/10.1142/9789812702371_0004 es_ES
dc.description.references S. B. Nadler, Sequence of contraction and fixed points, Pacific J.Math. 27 (1968), 579-585. es_ES
dc.description.references H. K. Nashinea, M. Imdadb and M. Hasan, Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear Sci. Appl. 7 (2014), 42-50. https://doi.org/10.22436/jnsa.007.01.05 es_ES
dc.description.references B. G. Pachpatte, Common fixed point theorems for mappings satisfying rational inequalities, Indian J. Pure appl. Math. 10, no. 11 (1979), 1362-1368. es_ES
dc.description.references A.-D. Filip and A. Petrusel, Fixed point theorems for operators in generalized Kasahara spaces, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas 109, no. 1 (2015), 15-26. https://doi.org/10.1007/s13398-014-0163-9 es_ES
dc.description.references M. Pitchaimani and D. Ramesh Kumar, Some common fixed point theorems using implicit relation in 2-Banach spaces, Surv. Math. Appl. 10 (2015), 159-168. es_ES
dc.description.references M. Pitchaimani and D. Ramesh Kumar, Common and coincidence fixed point theorems for asymptotically regular mappings in 2-Banach Spaces, Nonlinear Funct. Anal. Appl.21, no. 1 (2016), 131-144. es_ES
dc.description.references M. Pitchaimani and D. Ramesh Kumar, On construction of fixed point theory under implicit relation in Hilbert spaces, Nonlinear Funct. Anal. Appl. 21, no. 3 (2016), 513-522. es_ES
dc.description.references M. Pitchaimani and D. Ramesh Kumar, On Nadler type results in ultrametric spaces with application to well-posedness, Asian-European Journal of Mathematics 10, no. 4(2017), 1750073(1-15). https://doi.org/10.1142/s1793557117500735 es_ES
dc.description.references M. Pitchaimani and D. Ramesh Kumar, Generalized Nadler type results in ultrametric spaces with application to well-posedness, Afr. Mat. 28 (2017), 957-970. https://doi.org/10.1007/s13370-017-0496-6 es_ES
dc.description.references V. Popa, Well-Posedness of fixed problem in compact metric space, Bull. Univ. Petrol-Gaze, Ploicsti, sec. Mat Inform. Fiz. 60, no. 1 (2008), 1-4. es_ES
dc.description.references D. Ramesh Kumar and M. Pitchaimani, Set-valued contraction mappings of Presic-Reichtype in ultrametric spaces, Asian-European Journal of Mathematics 10, no. 4 (2017), 1750065 (1-15). https://doi.org/10.1142/s1793557117500656 es_ES
dc.description.references D. Ramesh Kumar and M. Pitchaimani, A generalization ofset-valued Presic-Reich type contractions in ultrametric spaces with applications, J. Fixed Point Theory Appl. 19,no. 3 (2017), 1871-1887. https://doi.org/10.1007/s11784-016-0338-4 es_ES
dc.description.references D. Ramesh Kumar and M. Pitchaimani, Approximation and stability of common fixed points of Presic type mappings in ultrametric spaces, J. Fixed Point Theory Appl. 20:4(2018). https://doi.org/10.1007/s11784-018-0504-y es_ES
dc.description.references D. Ramesh Kumar and M. Pitchaimani, New coupled fixed point theorems in cone metric spaces with applications to integral equations and Markov process, Transactions of A. Razmadze Mathematical Institute, to appear. https://doi.org/10.1016/j.trmi.2018.01.006 es_ES
dc.description.references S. Reich and A. T. Zaslawski, Well- Posedness of fixed point problems, Far East J. Math.sci, Special volume part III (2011), 393-401. es_ES
dc.description.references W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl. 2012, no. 1 (2012), 1-12. https://doi.org/10.1186/1029-242x-2012-84 es_ES
dc.description.references R. J. Shahkoohi and A. Razani, Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces, J. Inequal. Appl. 2014, no. 1 (2014), 1-23. https://doi.org/10.1186/1029-242x-2014-373 es_ES
dc.description.references S. Shukla, Presic type results in 2-Banach spaces Afr. Mat. 25, no. 4 (2014), 1043-1051. https://doi.org/10.1007/s13370-013-0174-2 es_ES
dc.description.references A. White, 2-Banach spaces, Math. Nachr. 42 (1969), 43-60. es_ES


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