Abstract
In this section we present fundamental definitions and elementary results (see Apostol [23], Bourbaki [51], and Schweizer and Sklar [186]).
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Bibliography
Agarwal, R., Karapınar, E., Roldán López-de-Hierro, A.F.: Fixed point theorems in quasi-metric spaces and applications to multidimensional fixed points on G-metric spaces. J. Nonlinear Convex Anal. 16, 1787–1816 (2015)
Apostol, T.: Mathematical Analysis. Addison-Wesley, Reading (1974)
Berinde, V.: Iterative Approximation of Fixed Points. Editura Efemeride, Baia Mare (2002)
Berinde, V.: Contracţii generalizate şi aplicaţii. Editura Cub Press 22, Baia Mare, Romania
Berinde, V.: A common fixed point theorem for compatible quasi contractive self mappings in metric spaces. Appl. Math. Comput. 213, 348–354 (2009)
Bianchini, R.M., Grandolfi, M.: Transformazioni di tipo contracttivo generalizzato in uno spazio metrico. Atti Acad. Naz. Lincei, VII. Ser., Rend., Cl. Sci. Fis. Mat. Natur. 45, 212–216 (1968)
Bourbaki, N.: Topologie générale. Herman, Paris (1961)
Boyd, D.W., Wong, J.S.W.: On nonlinear contractions. Proc. Am. Math. Soc. 20, 458–464 (1969)
Jleli, M., Samet, B.: Remarks on G-metric spaces and fixed point theorems. Fixed Point Theory Appl. 2012, 210 (2012)
Khan, M.S., Swaleh, M., Sessa, S.: Fixed point theorems by altering distances between the points. Bull. Aust. Math. Soc. 30, 1–9 (1984)
Lakshmikantham, V., Ćirić, Lj.B.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70, 4341–4349 (2009)
Matkowski, J.: Fixed point theorems for mappings with a contractive iterate at a point. Proc. Am. Math. Soc. 62, 344–348 (1977)
Mukherjea, A.: Contractions and completely continuous mappings. Nonlinear Anal. 1(3), 235–247 (1997)
Proinov, P.D.: A generalization of the Banach contraction principle with high order of convergence of successive approximations. Nonlinear Anal. 67, 2361–2369 (2007)
Proinov, P.D.: New general convergence theory for iterative processes and its applications to Newton Kantorovich type theorems. J. Complex. 26, 3–42 (2010)
Rus, I.A.: Generalized Contractions and Applications. Cluj University Press, Cluj-Napoca (2001)
Schweizer, B., Sklar, A.: Probabilistic Metric Spaces. Dover Publications, New York (2005)
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Agarwal, R.P., Karapınar, E., O’Regan, D., Roldán-López-de-Hierro, A.F. (2015). Preliminaries. In: Fixed Point Theory in Metric Type Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-24082-4_2
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DOI: https://doi.org/10.1007/978-3-319-24082-4_2
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