Some Fixed Point Theorems Via Combination of Weak Contraction and Caristi Contractive Mapping

[1] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 1922, 133–181.10.4064/fm-3-1-133-181Search in Google Scholar

[2] V. Berinde, Approximating fixed points of weak contractions using the Picard iteration, Nonlinear Anal. Forum 9 2004, no. 1, 43–53.Search in Google Scholar

[3] J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 1976, 241–251.10.1090/S0002-9947-1976-0394329-4Search in Google Scholar

[4] L.B. Ćirić, Generalized contractions and fixed-point theorems, Publ. Inst. Math. (Beograd) (N.S.) 12(26) 1971, 19–26.Search in Google Scholar

[5] L.B. Ćirić, A generalization of Banach’s contraction principle, Proc. Amer. Math. Soc. 45 1974, 267–273.10.1090/S0002-9939-1974-0356011-2Search in Google Scholar

[6] G.S. Jeong and B.E. Rhoades, Maps for which F(T) = F(Tⁿ), in: Y.J. Cho et al. (eds.), Fixed Point Theory and Applications, 6, Nova Sci. Publ., New York, 2007, pp. 71–104.Search in Google Scholar

[7] E. Karapınar, F. Khojasteh, and Z.D. Mitrovic, A proposal for revisiting Banach and Caristi type theorems in b-metric spaces, Mathematics 7 2019, no. 4, 308, 4 pp. DOI:10.3390/math7040308.10.3390/math7040308Search in Google Scholar

[8] E. Karapınar, F. Khojasteh, and W. Shatanawi, Revisiting Ćirić -type contraction with Caristi’s approach, Symmetry 11 2019, no. 6, 726, 7 pp. DOI:10.3390/sym11060726.10.3390/sym11060726Search in Google Scholar

[9] K. Roy and M. Saha, Fixed point theorems for generalized contractive and expansive type mappings over a C^*-algebra valued metric space, Sci. Stud. Res. Ser. Math. Inform. 28 2018, no. 1, 115–129.Search in Google Scholar

[10] K. Roy and M. Saha, Fixed point theorems for a pair of generalized contractive mappings over a metric space with an application to homotopy, Acta Univ. Apulensis Math. Inform. 60 2019, 1–17.Search in Google Scholar