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Some fixed point results for a generalized ψ-weak contraction mappings in orbitally metric spaces

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  • Shatanawi, Wasfi

Abstract

Samet and Vetro [Samet B, Vetro C. Berinde mappings in orbitally complete metric spaces. Chaos Solitons Fract 2011;44:1075–9.] studied a fixed point theorem for a self-mapping satisfying a general contractive condition of integral type in orbitally complete metric spaces. In this paper, we introduce the notion of a generalized ψ-weak contraction mapping and establish some results in orbitally complete metric spaces. Our results generalize several well-known comparable results in the literature. As an application of our results we deduce the result of Samet and Vetro. Some examples are given to illustrate the useability of our results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:45:y:2012:i:4:p:520-526
    DOI: 10.1016/j.chaos.2012.01.015
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    References listed on IDEAS

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    1. P. Vijayaraju & B. E. Rhoades & R. Mohanraj, 2005. "A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-6, January.
    2. Samet, Bessem & Vetro, Calogero, 2011. "Berinde mappings in orbitally complete metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 44(12), pages 1075-1079.
    3. B. E. Rhoades, 2003. "Two fixed-point theorems for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-7, January.
    4. 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.
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    Cited by:

    1. Abdolsattar Gholidahneh, & Shaban Sedghi, 2017. "Tripled Coincidence Point Results for $(\psi,\varphi)$-weakly Contractive Mappings in Partially Ordered S-matric Spaces," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 9(5), pages 108-125, October.
    2. Wasfi Shatanawi, 2018. "Common Fixed Points for Mappings under Contractive Conditions of ( α , β , ψ )-Admissibility Type," Mathematics, MDPI, vol. 6(11), pages 1-11, November.
    3. Vahid Parvaneh & Babak Mohammadi & Hassen Aydi & Aiman Mukheimer, 2019. "Generalized ( σ , ξ )-Contractions and Related Fixed Point Results in a P.M.S," Mathematics, MDPI, vol. 7(5), pages 1-14, May.
    4. Hasanen A. Hammad & Amal A. Khalil, 2020. "The Technique of Quadruple Fixed Points for Solving Functional Integral Equations under a Measure of Noncompactness," Mathematics, MDPI, vol. 8(12), pages 1-21, November.

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