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Existence and Ulam–Hyers stability of fixed point problem of generalized Suzuki type \(( \alpha _{*}{,\psi }_{\varphi })\)-contractive multivalued operators

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The aim of this paper is to introduce a class of generalized Suzuki type \( (\alpha _{*},\psi _{\varphi })\)-contractive multivalued operators and to prove the existence of fixed point and common fixed point of such operators in the setup of b-metric spaces. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature. An estimate of Hausdorff distance between the fixed point sets of two generalized Suzuki type \((\alpha _{*},\psi _{\varphi })\)-contractive multivalued operators is obtained. We further investigate the Ulam–Hyers stability of fixed point problem of operators considered herein in the framework of b-metric spaces.

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Acknowledgements

The authors are grateful to the reviewers for their valuable remarks and suggestions as it helped us to improve the original version of the paper.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood road, Pretoria, 0002, South Africa

    Basit Ali & Mujahid Abbas

  2. Department of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah, Saudi Arabia

    Mujahid Abbas

Authors
  1. Basit Ali
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  2. Mujahid Abbas
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Correspondence to Basit Ali.

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Ali, B., Abbas, M. Existence and Ulam–Hyers stability of fixed point problem of generalized Suzuki type \(( \alpha _{*}{,\psi }_{\varphi })\)-contractive multivalued operators. RACSAM 111, 1129–1146 (2017). https://doi.org/10.1007/s13398-016-0351-x

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  • DOI: https://doi.org/10.1007/s13398-016-0351-x

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