On new existence and uniqueness results concerning solutions to nonlinear Fredholm integral equations via w-distances and weak altering distance functions

  • Teerawat Wongyat
  • Wutiphol SintunavaratEmail author


The purpose of this work is to establish new fixed point theorems for generalized contraction mappings with respect to w-distances in complete metric spaces by using the concept of a weak altering distance function. Two illustrative examples are provided to advocate the usability of our results. Also, we present a numerical experiment for approximating a fixed point in these examples. As an application, the received results are used to summarize the existence and uniqueness of the solution for nonlinear Fredholm integral equations.


w-Distance altering distance weak altering distance nonlinear Fredholm integral equation 

Mathematics Subject Classification

Primary 47H10 Secondary 54H25 



The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under Grant no. MRG6180283 for financial support during the preparation of this manuscript.

Author Contributions

All authors contributed equally and significantly in writing this paper. All authors read and approved the final manuscript.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no competing interests.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.Department of Mathematics and Statistics Faculty of Science and TechnologyThammasat University Rangsit CenterKhlong LuangThailand

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