Interpolative Reich–Rus–Ćirić Type Contractions on Partial Metric Spaces

By E. Karapınar, Ravi P. Agarwal, Hassen Aydi. Mathematics, 2018

182 citations recorded by the source corpus.

By giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85–87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich–Rus–Ćirić in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121–124; Boll. Unione Mat. Ital. 1972, 4, 26–42 and Boll. Unione Mat. Ital. 1971, 4, 1–11.) is not applicable.

Subfields: Astronomy and Astrophysics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/bbc319e2062c5f36d52403cf5af1f04c4e20fdf2

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1. Aydi
2. Karapinar
3. Rakočević
4. Alqahtani

Citations in the corpus

• A Solution for Volterra Fractional Integral Equations by Hybrid Contractions (2019, background): “Using Corollary 3, we get Theorem 2 in [7] (for metric spaces).”