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Approximate fixed point theorems for partial generalized convex contraction mappings in \(\alpha\)-complete metric spaces. (English) Zbl 1357.54034

Summary: In this paper, we introduce the new concept called partial generalized convex contractions and partial generalized convex contractions of order 2. Also, we establish some approximate fixed point theorems for such mappings in \(\alpha\)-complete metric spaces. Our results extend and unify the results of M. Miandaragh et al. [Fixed Point Theory Appl. 2013, Paper No. 255, 8 p. (2013; Zbl 1321.54089)] and several well-known results in literature. We give some examples of a nonlinear contraction mapping, which is not applied to the existence of approximate fixed point and fixed point by using the results of Miandaragh et al. We also consider approximate fixed point results in metric space endowed with an arbitrary binary relation and approximate fixed point results in metric space endowed with graph.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces

Citations:

Zbl 1321.54089
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References:

[1] S. Banach, Sur les op’erations dans les ensembles abstraits et leurs applications aux ’equations int’egrales, Fund. Math., 3 (1922), 133-181. · JFM 48.0201.01
[2] M. Berinde, Approximate fixed point theorems, Stud. Univ. Babes Bolyai, Math., 51(1) (2006), 11-25. · Zbl 1164.54028
[3] F. E. Browder and W. V. Petrysyn, The solution by iteration of nonlinear functional equation in Banach spaces, Bull. Amer. Math. Soc., 72 (1966), 571-576.
[4] D. Dey and M. Saha, Approximate fixed point of Reich operator, Acta Mathematica Universitatis Comenianae, 82(1) (2013), 119-123. · Zbl 1324.54067
[5] D. Dey, A. K. Laha and M. Saha, Approximate coincidence point of two nonlinear mappings, Journal of Mathematics, Vol. 2013, Article ID 962058, 4 pages. · Zbl 1268.54022
[6] N. Hussain, M. A. Kutbi and P. Salimi, Fixed Point Theory in {\(\alpha\)}-complete Metric Spaces with Applications, Abstract and Applied Analysis, Vol. 2014, Article ID 280817, 11 Approximate Fixed Point Theorems for Partial Generalized Convex Contraction Mappings333
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