- -

Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

RiuNet: Repositorio Institucional de la Universidad Politécnica de Valencia

Compartir/Enviar a

Citas

Estadísticas

  • Estadisticas de Uso

Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces

Mostrar el registro sencillo del ítem

Ficheros en el ítem

Thumbnail
Nombre: Okeke;Abbas - Fejér ...
Tamaño: 472.0Kb
Formato: PDF
Descripción: Versión editorial
Abrir
dc.contributor.author Okeke, Godwin Amechi es_ES
dc.contributor.author Abbas, Mujahid es_ES
dc.date.accessioned 2020-04-27T09:31:40Z
dc.date.available 2020-04-27T09:31:40Z
dc.date.issued 2020-04-03
dc.identifier.issn 1576-9402
dc.identifier.uri http://hdl.handle.net/10251/141565
dc.description.abstract [EN] It is our purpose in this paper to prove some fixed point results and Fej´er monotonicity of some faster fixed point iterative sequences generated by some nonlinear operators satisfying rational inequality in complex valued Banach spaces. We prove that results in complex valued Banach spaces are valid in cone metric spaces with Banach algebras. Furthermore, we apply our results in solving certain mixed type VolterraFredholm functional nonlinear integral equation in complex valued Banach spaces. es_ES
dc.description.sponsorship The first author’s research is supported by the Abdus Salam School of Mathematical Sciences, Government College University, Lahore, Pakistan through grant number: ASSMS/2018-2019/452. es_ES
dc.language Inglés es_ES
dc.publisher Universitat Politècnica de València es_ES
dc.relation.ispartof Applied General Topology es_ES
dc.rights Reconocimiento - No comercial - Sin obra derivada (by-nc-nd) es_ES
dc.subject Complex valued Banach spaces es_ES
dc.subject Fixed point theorems es_ES
dc.subject Féjer monotonicity es_ES
dc.subject Iterative processes es_ES
dc.subject Cone metric spaces with Banach algebras es_ES
dc.subject Mixed type Volterra-Fredholm functional nonlinear integral equation es_ES
dc.title Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.4995/agt.2020.12220
dc.relation.projectID info:eu-repo/grantAgreement/ASSMS//2018-2019%2F452/
dc.rights.accessRights Abierto es_ES
dc.description.bibliographicCitation Okeke, GA.; Abbas, M. (2020). Fejér monotonicity and fixed point theorems with applications to a nonlinear integral equation in complex valued Banach spaces. Applied General Topology. 21(1):135-158. https://doi.org/10.4995/agt.2020.12220 es_ES
dc.description.accrualMethod OJS es_ES
dc.relation.publisherversion https://doi.org/10.4995/agt.2020.12220 es_ES
dc.description.upvformatpinicio 135 es_ES
dc.description.upvformatpfin 158 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 21 es_ES
dc.description.issue 1 es_ES
dc.identifier.eissn 1989-4147
dc.relation.pasarela OJS\12220 es_ES
dc.contributor.funder Abdus Salam School of Mathematical Sciences es_ES
dc.description.references M. Abbas and B. E. Rhoades, Fixed and periodic point results in cone metric spaces, Appl. Math. Lett. 22 (2009), 511-515. https://doi.org/10.1016/j.aml.2008.07.001 es_ES
dc.description.references M. Abbas, V. C. Rajic, T. Nazir and S. Radenovic, Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afr. Mat. 2013, 14 pages. https://doi.org/10.1007/s13370-013-0185-z es_ES
dc.description.references M. Abbas, M. Arshad and A. Azam, Fixed points of asymptotically regular mappings in complex-valued metric spaces, Georgian Math. J. 20 (2013), 213-221. https://doi.org/10.1515/gmj-2013-0013 es_ES
dc.description.references M. Abbas and T. Nazir, A new faster iteration process applied to constrained minimization and feasibility problems, Mat. Vesn. 66 (2014), 223-234. es_ES
dc.description.references M. Abbas, M. De la Sen and T. Nazir, Common fixed points of generalized cocyclic mappings in complex valued metric spaces, Discrete Dynamics in Nature and Society 2015, Article ID: 147303, 2015, 11 pages. https://doi.org/10.1155/2015/147303 es_ES
dc.description.references W. M. Alfaqih, M. Imdad and F. Rouzkard, Unified common fixed point theorems in complex valued metric spaces via an implicit relation with applications, Bol. Soc. Paran. Mat. (3s.) 38, no. 4 (2020), 9-29. https://doi.org/10.5269/bspm.v38i4.37148 es_ES
dc.description.references R. P. Agarwal, D. O'Regan and D.R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, Journal of Nonlinear and Convex Analysis 8, no. 1 (2007), 61-79. es_ES
dc.description.references J. Ahmad, N. Hussain, A. Azam and M. Arshad, Common fixed point results in complex valued metric space with applications to system of integral equations, Journal of Nonlinear and Convex Analysis 29, no. 5 (2015), 855-871. es_ES
dc.description.references H. Akewe, G. A. Okeke and A. F. Olayiwola, Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators, Fixed Point Theory and Applications 2014, 2014:46, 24 pages. https://doi.org/10.1186/1687-1812-2014-45 es_ES
dc.description.references H. Akewe and G. A. Okeke, Convergence and stability theorems for the Picard-Mann hybrid iterative scheme for a general class of contractive-like operators, Fixed Point Theory and Applications (2015) 2015:66, 8 pages. https://doi.org/10.1186/s13663-015-0315-4 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 leurs applications aux équations intégrales, Fund. Math. 3, (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181 es_ES
dc.description.references H. H. Bauschke and P. L. Combettes, Convex analysis and monotone operator theory in Hilbert spaces, CMS Books in Mathematics, Second Edition, Springer International Publishing AG, 2017. https://doi.org/10.1007/978-3-319-48311-5_2 es_ES
dc.description.references V. Berinde, Summable almost stability of fixed point iteration procedures, Carpathian J. Math. 19, no. 2 (2003), 81-88. es_ES
dc.description.references V. Berinde, Iterative approximation of fixed points, Lecture Notes in Mathematics, Springer-Verlag Berlin Heidelberg, 2007. https://doi.org/10.1109/SYNASC.2007.49 es_ES
dc.description.references A. Cegielski, Iterative methods for fixed point problems in Hilbert spaces, Lecture Notes in Mathematics, Springer Heidelberg New York Dordrecht London, 2012. https://doi.org/10.1007/978-3-642-30901-4 es_ES
dc.description.references R. Chugh, V. Kumar and S. Kumar, Strong convergence of a new three step iterative scheme in Banach spaces, American Journal of Computational Mathematics 2 (2012), 345-357. https://doi.org/10.4236/ajcm.2012.24048 es_ES
dc.description.references C. Craciun and M.-A. Serban, A nonlinear integral equation via Picard operators, Fixed Point Theory 12, no. 1 (2011), 57-70. es_ES
dc.description.references F. Gürsoy, Applications of normal S-iterative method to a nonlinear integral equation, The Scientific World Journal 2014, Article ID 943127, 2014, 5 pages. https://doi.org/10.1155/2014/943127 es_ES
dc.description.references F. Gürsoy and V. Karakaya, A Picard-S hybrid type iteration method for solving a differential equation with retarded argument, arXiv:1403.2546v2 [math.FA] 2014. es_ES
dc.description.references B. K. Dass and S. Gupta, An extension of Banach contraction principle through rational expression, Indian J. Pure Appl. Math. 6 (1975), 1455-1458. es_ES
dc.description.references B. C. Dhage, Generalized metric spaces with fixed point, Bull. Calcutta Math. Soc. 84 (1992), 329-336. 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 (2007), 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087 es_ES
dc.description.references N. Hussain, V. Kumar and M. A. Kutbi, On rate of convergence of Jungck-type iterative schemes, Abstract and Applied Analysis 2013, Article ID 132626, 15 pages. https://doi.org/10.1155/2013/132626 es_ES
dc.description.references H. Humaira, M. Sarwar and P. Kumam, Common fixed point results for fuzzy mappings on complex-valued metric spaces with homotopy results, Symmetry 11, no. 1 (2019),17 pages. https://doi.org/10.3390/sym11010061 es_ES
dc.description.references S. Ishikawa, Fixed points by a new iteration method, Proc. Am. Math. Soc. 44 (1974), 147-150. https://doi.org/10.1090/S0002-9939-1974-0336469-5 es_ES
dc.description.references I. Karahan and M. Ozdemir, A general iterative method for approximation of fixed points and their applications, Advances in Fixed Point Theory 3 (2013), 510-526. https://doi.org/10.1186/1687-1812-2013-244 es_ES
dc.description.references S. H. Khan, A Picard-Mann hybrid iterative process, Fixed Point Theory and Applications 2013, 2013:69, 10 pages. https://doi.org/10.1186/1687-1812-2013-69 es_ES
dc.description.references H. Liu and S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory and Appl. 2013, 2013:320, 10 pages. https://doi.org/10.1186/1687-1812-2013-320 es_ES
dc.description.references W. R. Mann, Mean value methods in iteration, Proc. Am. Math. Soc. 4 (1953), 506-510. https://doi.org/10.1090/S0002-9939-1953-0054846-3 es_ES
dc.description.references M. A. Noor, New approximation schemes for general variational inequalities, J. Math. Anal. Appl. 251 (2000), 217-229. https://doi.org/10.1006/jmaa.2000.7042 es_ES
dc.description.references G. A. Okeke, Iterative approximation of fixed points of contraction mappings in complex valued Banach spaces, Arab. J. Math. Sci. 25, no. 1 (2019), 83-105. https://doi.org/10.1016/j.ajmsc.2018.11.001 es_ES
dc.description.references G. A. Okeke and M. Abbas, A solution of delay differential equations via Picard-Krasnoselskii hybrid iterative process, Arab. J. Math. 6 (2017), 21-29. https://doi.org/10.1007/s40065-017-0162-8 es_ES
dc.description.references M. Öztürk and M. Basarir, On some common fixed point theorems with rational expressions on cone metric spaces over a Banach algebra, Hacettepe J. Math. and Stat. 41, no. 2 (2012), 211-222. es_ES
dc.description.references W. Phuengrattana and S. Suantai, On the rate of convergence of Mann, Ishikawa, Noor and SP-iterations for continuous functions on an arbitrary interval, Journal of Computational and Applied Mathematics 235 (2011), 3006-3014. https://doi.org/10.1016/j.cam.2010.12.022 es_ES
dc.description.references F. Rouzkard and M. Imdad, Some common fixed point theorems on complex valued metric spaces, Computers and Mathematics with Applications 64 (2012), 1866-1874. https://doi.org/10.1016/j.camwa.2012.02.063 es_ES
dc.description.references W. Rudin, Functional analysis, 2nd edn. McGraw-Hill, New York, 1991. es_ES
dc.description.references D. R. Sahu and A. Petrusel, Strong convergence of iterative methods by strictly pseudocontractive mappings in Banach spaces, Nonlinear Analysis: Theory, Methods & Applications 74, no. 17 (2011), 6012-6023. https://doi.org/10.1016/j.na.2011.05.078 es_ES
dc.description.references B. Samet, C. Vetro and H. Yazidi, A fixed point theorem for a Meir-Keeler type contraction through rational expression, J. Nonlinear Sci. Appl. 6 (2013), 162-169. https://doi.org/10.22436/jnsa.006.03.02 es_ES
dc.description.references S. Shukla, R. Rodríguez-López and M. Abbas, Fixed point results for contractive mappings in complex valued fuzzy metric spaces, Fixed Point Theory 19, no. 2 (2018), 751-774. es_ES
dc.description.references N. Singh, D. Singh, A. Badal and V. Joshi, Fixed point theorems in complex valued metric spaces, Journal of the Egyptian Math. Soc. 24 (2016), 402-409. https://doi.org/10.1016/j.joems.2015.04.005 es_ES
dc.description.references W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Ineq. Appl. 2012, 2012:84' 12 pages. https://doi.org/10.1186/1029-242X-2012-84 es_ES
dc.description.references S. M. Soltuz and T. Grosan, Data dependence for Ishikawa iteration when dealing with contractive-like operators, Fixed Point Theory and Applications 2008, Article ID 242916, 2008, 7 pages. https://doi.org/10.1155/2008/242916 es_ES
dc.description.references B. S. Thakur, D. Thakur and M. Postolache, A new iterative scheme for numerical reckoning fixed points of Suzuki's generalized nonexpansive mappings, App. Math. Comp. 275 (2016), 147-155. https://doi.org/10.1016/j.amc.2015.11.065 es_ES
dc.description.references K. Ullah and M. Arshad, Numerical reckoning fixed points for Suzuki's generalized nonexpansive mappings via new iteration process, Filomat 32, no. 1 (2018), 187-196. https://doi.org/10.2298/FIL1801187U es_ES


Este ítem aparece en la(s) siguiente(s) colección(ones)

Mostrar el registro sencillo del ítem