Fixed point results of enriched interpolative Kannan type operators with applications

• Abbas, Mujahid ^[1] ; Anjum, Rizwan ^[2] ; Riasat, Shakeela ^[3]
  1. [1] University of Pretoria

     University of Pretoria

     City of Tshwane, Sudáfrica

     
  2. [2] Riphah International University

     Riphah International University

     Pakistán

     
  3. [3] Government College University

  Mostrar afiliaciones +
• Localización: Applied general topology, ISSN-e 1989-4147, ISSN 1576-9402, Vol. 23, Nº. 2, 2022, págs. 391-404
• Idioma: inglés
• DOI: 10.4995/agt.2022.16701
• Enlaces
  • Texto completo
• Resumen

  • The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains theclasses of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskij iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problems is solved.

• Referencias bibliográficas
  • R. Anjum and M. Abbas, Fixed point property of a nonempty set relative to the class offriendly mappings, Rev. R. Acad. Cienc. Exactas Fıs....
  • R. Anjum and M. Abbas, Common fixed point theorem for modified Kannan enrichedcontraction pair in Banach spaces and its applications, Filomat...
  • M. Abbas, R. Anjum and V. Berinde, Enriched multivalued contractions with applica-tions to differential inclusions and dynamic programming,...
  • M. Abbas, R. Anjum and V. Berinde, Equivalence of certain iteration processes obtainedby two new classes of operators, Mathematics 9, no....
  • M. Abbas, R. Anjum and H. Iqbal, Generalized enriched cyclic contractions with appli-cation to generalized iterated function system, Chaos,...
  • R. P. Agarwal and E. Karapinar, Interpolative Rus-Reich- Ciric type contractions viasimulation functions, An. St. Univ. Ovidius Constanta,...
  • R. P. Agarwal, E. Karapinar, D. O'Regan and A. F. Roldan Lopez de Hierro, Fixedpoint theory in metric type spaces, Springer International...
  • H. Aydi, E. Karapinar and A. F. Roldan Lopez de Hierro, w-Interpolative Ciric-Reich-Rus-type contractions, Mathematics 7, no. 57 (2019), Paper...
  • H. Aydi, C. M. Chen and E. Karapinar, Interpolative Ciric-Reich-Rustypes via the Branciari distance, Mathematics 7, no. 1 (2019), Paper no....
  • F. S. D. Blasi and J. Myjak, Sur la porosité de l'ensemble des contractions sans point fixe, C. R. Acad. Sci. Paris. 308 (1989), 51-54.
  • V. Berinde and M. Păcurar, Approximating fixed points of enriched contractions in Banach spaces, Journal of Fixed Point Theory and Applications...
  • V. Berinde and M. Păcurar, Kannan's fixed point approximation for solving split feasibility and variational inequality problems, Journal...
  • V. Berinde, Approximating fixed points of enriched nonexpansive mappings by Krasnoselskii iteration in Hilbert spaces, Carpathian J. Math....
  • V. Berinde and M. Păcurar, Approximating fixed points of enriched Chatterjea contractions by Krasnoselskii iterative algorithm in Banach spaces,...
  • V. Berinde and M. Păcurar, Fixed point theorems for enriched Ćirić-Reich-Rus contractions in Banach spaces and convex metric spaces, Carpathian...
  • F. E. Browder and W. V. Petryshyn, The solution by iteration of nonlinear functional equations in Banach spaces, Bull. Am. Math. Soc. 72 (1966),...
  • C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Probl. 20, no. 1 (2004),...
  • E. Connell, Properties of fixed point spaces, Proc. Amer. Math. Soc. 10 (1959), 974-979. https://doi.org/10.1090/S0002-9939-1959-0110093-3
  • I. C. Chifu and E. Karapinar, Admissible hybrid Z-contractions in b-metric spaces, Axioms. 9, no. 1, (2020), Paper no. 2. https://doi.org/10.3390/axioms9010002
  • P. Debnath and M. de La Sen, Set-valued interpolative Hardy-Rogers and set-valued Reich-Rus-Ćirić-type contractions in b-metric spaces, Mathematics....
  • Y. U. Gaba and E. Karapinar, A new approach to the interpolative contractions, Axioms 8, no. 4 (2019), Paper no. 110. https://doi.org/10.3390/axioms8040110
  • Y. U. Gaba, H. Aydi and N. Mlaik, (ρ,η,μ)-interpolative Kannan contractions I, Axioms. 10, no. 3 (2021), Paper no. 212. https://doi.org/10.3390/axioms10030212
  • G. S. Jeong and B. E. Rhoades, Maps for which $F(T)=F(T^{n}),$ Fixed Point Thoery Appl. 6 (2005), 87-131.
  • J. Górnicki and R. K. Bisht, Around averaged mappings, Journal of Fixed Point Theory and Applications 23 (2021), Paper no. 48. https://doi.org/10.1007/s11784-021-00884-y
  • R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71-76. https://doi.org/10.2307/2316437
  • R. Kannan, Some results o fixed points, II, Amer. Math. Monthly 76 (1969), 405-408. https://doi.org/10.1080/00029890.1969.12000228
  • M. Kikkawa and T. Suzuki, Some similarity between contractions and Kannan mappings II, Bull. Kyushu Inst. Technol. Pure Appl. Math. 55 (2008)...
  • E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl. 2, no. 2 (2018), 85-87. https://doi.org/10.31197/atnaa.431135
  • E. Karapinar, O. Alqahtani and H. Aydi, On interpolative Hardy-Rogers type contractions, Symmetry. 11, no. 1 (2019), Paper no. 8. https://doi.org/10.3390/sym11010008
  • E. Karapinar, R. Agarwal and H. Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics 6, no. 11 (2018),...
  • E. Karapinar and A. Fulga, New hybrid contractions on b-metric spaces, Mathematics 7, no. 7 (2019), Paper no. 578. https://doi.org/10.3390/math7070578
  • E. Karapinar, H. Aydi and Z. D. Mitrovic, On interpolative Boyd-Wong and Matkowski type contractions, TWMS J. Pure Appl. Math. 11, no. 2 (2020),...
  • E. Karapinar, A. Fulga and A. F. Roldán López de Hierro, Fixed point theory in the setting of (α,β,ψ,ϕ)-interpolative contractions, Advances...
  • E. Karapinar, Interpolative Kannan-Meir-Keeler type contractions, Advances in the Theory of Nonlinear Analysis and its Applications 5, no....
  • M. S. Khan, Y. M. Singh and E. Karapinar, On the interpolative (ϕ,ψ)-type Z-contractions, U. P. B. Sci. Bull. Series A. 83, no. 2 (2021),...
  • E. Karapinar, A. Fulga and S. S. Yesilkaya, New Results on Perov-interpolative contractions of Suzuki type mappings, Journal of Functional...
  • M. A. Krasnoselskii, Two remarks on the method of successive approximations, Uspekhi Mat. Nauk. 10 (1955), 123-127.
  • M. Noorwali, Common fixed point for Kannan type via interpolation, J. Math. Anal. 9, no. 6 (2018), 92-94.
  • S. Reich and A. J. Zaslavski, Well-posedness of fixed point problems, Far East Journal of Mathematical Sciences (FJMS) 2001, Special volume,...
  • I. A. Rus, Generalized Contractions and Applications, Cluj University Press, Cluj-Napoca, 2001.
  • P. V. Subrahmanyam, Remarks on some fixed point theorems related to Banach's contraction principle, J. Math. Phys. Sci. 8 (1974), 445-457.
  • W. Sintunavarat, Generalized Ulam-Hyres stability, well-posedness and limit shadowing of fixed point problems for α-β-contraction mapping...