Research article

3D analysis of modified F-contractions in convex b-metric spaces with application to Fredholm integral equations

  • Received: 21 April 2020 Accepted: 26 August 2020 Published: 08 September 2020
  • MSC : 54H25

  • The article defines F-Reich contraction while eliminating the condition (F3) and (F4) of F-contraction of Nadler type defined by Cosentino and using generalized Mann's iteration algorithm, some interesting theorems are developed in the setting of convex b-metric spaces. Example are stated in support of our proved results and application of our results in finding solution point to Fredholm Integral equation of the second kind are given.

    Citation: Awais Asif, Sami Ullah Khan, Thabet Abdeljawad, Muhammad Arshad, Ekrem Savas. 3D analysis of modified F-contractions in convex b-metric spaces with application to Fredholm integral equations[J]. AIMS Mathematics, 2020, 5(6): 6929-6948. doi: 10.3934/math.2020444

    Related Papers:

  • The article defines F-Reich contraction while eliminating the condition (F3) and (F4) of F-contraction of Nadler type defined by Cosentino and using generalized Mann's iteration algorithm, some interesting theorems are developed in the setting of convex b-metric spaces. Example are stated in support of our proved results and application of our results in finding solution point to Fredholm Integral equation of the second kind are given.


    加载中


    [1] S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Univ. Ostrav., 1 (1993), 5-11.
    [2] L. Chen, C. Li, R. Kaczmarek, et al. Several fixed point theorems in convex b-metric spaces and applications, Mathematics, 8 (2020), 1-16.
    [3] A. Branciari, A fixed point theorem of Banach-Caccioppoli type on a class of generalized metric spaces, Publ. Math. Debr., 57 (2000), 31-37.
    [4] R. Fagin, R. Kumar, D. Sivakumar, Comparing top k lists, SIAM J. Discrete Math., 17 (2003), 134-160.
    [5] V. S. Gahler, 2-metrische Raume und ihre topologische struktur, Math. Nachr., 26 (1963), 115-148.
    [6] A. Hussain, T. Kanwal, Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results, Tran. A. Razmadze Math. Institute, 172 (2018), 481-490.
    [7] M. Jleli, B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl., 2015 (2015), 1-14.
    [8] M. Jleli, B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl., 20 (2018), 128.
    [9] S. Malhotra, S. Shukla, R. Sen, Some fixed point theorems for ordered Reich type contractions in cone rectangular metric spaces, Acta Math. Univ. Comenianae, 2 (2013), 165-175.
    [10] S. G. Matthews, Partial metric topology, In: Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., 728 (1994), 183-197.
    [11] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297.
    [12] D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2012 (2012), 94.
    [13] M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers type, Filomat, 28 (2014), 715-722.
    [14] A. Shoaib, A. Asif, M. Arshad, Generalized dynamic process for generalized multivalued F-contraction of hardy Rogers type in b-metric spaces, Turk. J. Anal. Number Theory, 6 (2018), 43-48.
    [15] A. Asif, M. Nazim, M. Arshad, et al. F-metric, F-contraction and common fixed point theorems with applications, Mathematics, 7 (2019), 586-599.
    [16] Z. Ma, A. Asif, H. Aydi, et al. Analysis of F-contractions in function weighted metric spaces with an application, Open Math., 18 (2019), 582-594.
    [17] M. Cosentino, M. Jleli, B. samet, et al. Solvability of integrodifferential problems via fixed point theory in b-metric spaces, Fixed Point Theory App., 2015 (2015), 70.
    [18] W. H. Teukolsky, S. A. Vetterling, W. T. Flannery, Section 19.1. Fredholm Equations of the Second Kind, In: Numerical Recipes: The Art of Scientific Computing, 3 Eds., Cambridge University Press, New York, 2007.
  • Reader Comments
  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(2713) PDF downloads(90) Cited by(4)

Article outline

Figures and Tables

Figures(2)

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog