Abstract
In this paper, the notion of \((\varphi , F)\)-weak contractions in the framework of metric-like spaces is introduced and the corresponding fixed point theorems are established. As an attempt to answer the common question regarding the uniqueness of trivial solutions of homogeneous integral equations on time scales, one of our main results is applied to investigate sufficient criteria for existence and uniqueness of solution of nonlinear Fredholm integral equations of the second kind on time scales. The latter result is obtained through a new Lipschitz condition on the kernel different from the usual ones. Examples are constructed to show that our ideas herein are new and generalize some recently announced results in the literature.
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The authors are thankful to the editors and the anonymous reviewers for their valuable suggestions and comments that helped to improve this manuscript.
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MSS: conceptualization and writing, MA: carried out the proof of further consequences, applications and constructed some new special cases in form of corollaries, AA: review and editing, SK: review and editing. All authors have read and approved the final manuscript for submission and possible publication. All authors have also agreed to be personally and jointly accountable for their contributions to this manuscript.
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Mohammed, S.S., Alansari, M., Azam, A. et al. Fixed points of \((\varphi ,F)\)-weak contractions on metric-like spaces with applications to integral equations on time scales. Bol. Soc. Mat. Mex. 27, 39 (2021). https://doi.org/10.1007/s40590-021-00347-x
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DOI: https://doi.org/10.1007/s40590-021-00347-x