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New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations

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Abstract

In this paper, the notion of α-ψ-contractive mappings in the setting of w-distance is introduced and some new fixed point theorems for such mappings are established. Presented fixed point theorems generalize recent results of Samet et al. [Nonlinear Anal. 75 (2012), 2154–2165] and others. Moreover, some examples and an application to nonlinear fractional differential equations are given to illustrate the usability of the new theory.

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Authors and Affiliations

  1. Department of Mathematics, Payame Noor University, 19395-4697, Tehran, Iran

    Hossein Lakzian

  2. Department of Applied Mathematics & Humanities, S.V. National Institute of Technology, Surat, 395007, India

    Dhananjay Gopal

  3. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani, 12121, Thailand

    Wutiphol Sintunavarat

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  1. Hossein Lakzian
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  2. Dhananjay Gopal
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  3. Wutiphol Sintunavarat
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Correspondence to Wutiphol Sintunavarat.

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Lakzian, H., Gopal, D. & Sintunavarat, W. New fixed point results for mappings of contractive type with an application to nonlinear fractional differential equations. J. Fixed Point Theory Appl. 18, 251–266 (2016). https://doi.org/10.1007/s11784-015-0275-7

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  • DOI: https://doi.org/10.1007/s11784-015-0275-7

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