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

• Autores: D. Ramesh Kumar, M. Pitchaimani
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 20, Nº. 1, 2019, págs. 43-55
• Idioma: inglés
• DOI: 10.4995/agt.2019.9168
• Enlaces
  • Texto completo
• Resumen

  • 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.

• Referencias bibliográficas
  • M. Abbas, B. E. Rhoades and T. Nazir, Common fixed points for four maps in cone metric spaces, Applied Mathematics and Computation 216 (2010),...
  • M. Abbas and G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl....
  • M. Arshad, E. Karapinar and J. Ahmad, Some unique fixed point theorems for rational contractions in partially ordered metric spaces, J. Inequal....
  • A. Azam, B. Fisher and M. Khan, Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and optimization...
  • 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
  • I. Beg and A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal....
  • K. Cieplinski, Approximate multi-additive mappings in 2-Banach spaces, Bull. Iranian Math. Soc. 41, no. 3 (2015), 785–792.
  • 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),...
  • 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.
  • S. Gähler, 2-metrische Räume and ihre topologische strucktur, Math. Nachr. 26 (1963), 115–148. https://doi.org/10.1002/mana.19630260109
  • S. Gähler, Uber die unifromisieberkeit 2-metrischer Räume, Math. Nachr. 28 (1965), 235–244. https://doi.org/10.1002/mana.19640280309
  • S. Gähler, Über 2-Banach-Räume, Math. Nachr. 42 (1969), 335–347. https://doi.org/10.1002/mana.19690420414
  • 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....
  • 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
  • K. Iseki, Fixed point theorems in 2-metric space, Math.Seminar. Notes, Kobe Univ. 3(1975), 133–136.
  • E. Matouskova, S. Reich and A. J. Zaslavski, Genericity in nonexpansive mapping theory, Advanced Courses of Mathematical Analysis I, World...
  • S. B. Nadler, Sequence of contraction and fixed points, Pacific J.Math. 27 (1968), 579–585.
  • H. K. Nashinea, M. Imdadb and M. Hasan, Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear...
  • B. G. Pachpatte, Common fixed point theorems for mappings satisfying rational inequalities, Indian J. Pure appl. Math. 10, no. 11 (1979),...
  • A.-D. Filip and A. Petrusel, Fixed point theorems for operators in generalized Kasahara spaces, Revista de la Real Academia de Ciencias Exactas,...
  • M. Pitchaimani and D. Ramesh Kumar, Some common fixed point theorems using implicit relation in 2-Banach spaces, Surv. Math. Appl. 10 (2015),...
  • M. Pitchaimani and D. Ramesh Kumar, Common and coincidence fixed point theorems for asymptotically regular mappings in 2-Banach Spaces, Nonlinear...
  • M. Pitchaimani and D. Ramesh Kumar, On construction of fixed point theory under implicit relation in Hilbert spaces, Nonlinear Funct. Anal....
  • M. Pitchaimani and D. Ramesh Kumar, On Nadler type results in ultrametric spaces with application to well-posedness, Asian-European Journal...
  • M. Pitchaimani and D. Ramesh Kumar, Generalized Nadler type results in ultrametric spaces with application to well-posedness, Afr. Mat. 28...
  • V. Popa, Well-Posedness of fixed problem in compact metric space, Bull. Univ. Petrol-Gaze, Ploicsti, sec. Mat Inform. Fiz. 60, no. 1 (2008),...
  • D. Ramesh Kumar and M. Pitchaimani, Set-valued contraction mappings of Presic-Reichtype in ultrametric spaces, Asian-European Journal of Mathematics...
  • D. Ramesh Kumar and M. Pitchaimani, A generalization ofset-valued Presic-Reich type contractions in ultrametric spaces with applications,...
  • D. Ramesh Kumar and M. Pitchaimani, Approximation and stability of common fixed points of Presic type mappings in ultrametric spaces, J. Fixed...
  • D. Ramesh Kumar and M. Pitchaimani, New coupled fixed point theorems in cone metric spaces with applications to integral equations and Markov...
  • S. Reich and A. T. Zaslawski, Well- Posedness of fixed point problems, Far East J. Math.sci, Special volume part III (2011), 393–401.
  • W. Sintunavarat and P. Kumam, Generalized common fixed point theorems in complex valued metric spaces and applications, J. Inequal. Appl....
  • R. J. Shahkoohi and A. Razani, Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces, J. Inequal....
  • 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
  • A. White, 2-Banach spaces, Math. Nachr. 42 (1969), 43–60.