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A fixed point theorem for mappings satisfying a general contractive condition of integral type

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  • A. Branciari

Abstract

We analyze the existence of fixed points for mappings defined on complete metric spaces ( X , d ) satisfying a general contractive inequality of integral type. This condition is analogous to Banach-Caccioppoli's one; in short, we study mappings f : X → X for which there exists a real number c ∈ ] 0 , 1 [ , such that for each x , y ∈ X we have ∫ 0 d ( f x , f y ) φ ( t ) d t ≤ c ∫ 0 d ( x , y ) φ ( t ) d t , where φ : [ 0 , + ∞ [ → [ 0 , + ∞ ] is a Lebesgue-integrable mapping which is summable on each compact subset of [ 0 , + ∞ [ , nonnegative and such that for each ε > 0 , ∫ 0 ε φ ( t ) d t > 0 .

Suggested Citation

  • A. Branciari, 2002. "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    • Handle: RePEc:hin:jijmms:641824
    DOI: 10.1155/S0161171202007524
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    Cited by:

    1. Manish Jain & Neetu Gupta & Sanjay Kumar, 2014. "Coupled Fixed Point Theorems for ( )-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications," International Journal of Analysis, Hindawi, vol. 2014, pages 1-9, March.
    2. Mian Bahadur Zada & Muhammad Sarwar & Nayyar Mehmood, 2016. "Common Fixed Point Results for Six Mappings via Integral Contractions with Applications," International Journal of Analysis, Hindawi, vol. 2016, pages 1-13, October.
    3. Shatanawi, Wasfi, 2012. "Some fixed point results for a generalized ψ-weak contraction mappings in orbitally metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 45(4), pages 520-526.
    4. Nesrin Manav Tatar & Ravi P. Agarwal, 2023. "Best Approximation of Fixed-Point Results for Branciari Contraction of Integral Type on Generalized Modular Metric Space," Mathematics, MDPI, vol. 11(21), pages 1-15, October.
    5. Biljana Carić & Tatjana Došenović & Reny George & Zoran D. Mitrović & Stojan Radenović, 2021. "On Jungck–Branciari–Wardowski Type Fixed Point Results," Mathematics, MDPI, vol. 9(2), pages 1-11, January.
    6. Mustafa Mudhesh & Aftab Hussain & Muhammad Arshad & Hamed Alsulami, 2023. "A Contemporary Approach of Integral Khan-Type Multivalued Contractions with Generalized Dynamic Process and an Application," Mathematics, MDPI, vol. 11(20), pages 1-18, October.
    7. Lakzian, Hossein & Rhoades, B.E., 2019. "Some fixed point theorems using weaker Meir–Keeler function in metric spaces with w−distance," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 18-25.
    8. Samet, Bessem & Vetro, Calogero, 2011. "Berinde mappings in orbitally complete metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1075-1079.
    9. Muhammad Shoaib & Muhammad Sarwar & Sultan Hussain & Gohar Ali, 2017. "Existence and Uniqueness of Common Fixed Point for Mappings Satisfying Integral Type Contractive Conditions in G-Metric Spaces," Matrix Science Mathematic (MSMK), Zibeline International Publishing, vol. 1(1), pages 1-8, January.
    10. Ghosh, S.K. & Nahak, C., 2020. "An extension of Lakzian-Rhoades results in the structure of ordered b-metric spaces via wt-distance with an application," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    11. Kobkoon Janngam & Suthep Suantai, 2022. "An Inertial Modified S-Algorithm for Convex Minimization Problems with Directed Graphs and Its Applications in Classification Problems," Mathematics, MDPI, vol. 10(23), pages 1-15, November.
    12. J. R. Morales & E. M. Rojas, 2012. "Some Generalizations of Jungck's Fixed Point Theorem," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-19, November.

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