A Study on Some Multi-Valued Interpolative Contractions

Year 2020, Volume: 3 Issue: 4, 208 - 217, 22.12.2020

Seher Sultan YEŞİLKAYA Cafer AYDIN Yaşar ASLAN

https://doi.org/10.33434/cams.794172

Cited By: 2

Abstract

In the present study, we introduce a new approach to interpolative mappings in fixed point theory by combining the ideas of Nadler [1], Karapınar et. al. [2,3], Jleli and Samet [4]. We introduce some fixed point theorems for interpolative single and multi-valued Kannan type and Reich Rus Ciric type $\theta$-contractive mappings on complete metric spaces and prove some fixed point results for these mappings. These results extend the main results of many comparable results from the current literature. Also, we give an example to show that our main theorems are applicable.

Keywords

Fixed point, Metric spaces, Multi-valued contractive mapping

References

• [1] S.B. Nadler, Multivalued contraction mappings, Pacific Journal of Mathematics, 30 (1969), 475-488.
• [2] E. Karapınar, Revisiting the Kannan type contractions via interpolation, Advances in the Theory of Nonlinear Analysis and its Applications, 2 (2018), 85-87.
• [3] E. Karapınar, R.P. Agarwal, H. Aydi, Interpolative Reich-Rus-Ciric Type Contractions on Partial Metric Spaces, Mathematics, 6(11) (2018), 256.
• [4] M. Jleli, B. Samet, A new generalization of the Banach contraction principle, Journal of Inequalities and Applications, 38 (2014), 1-8.
• [5] S. Banach, Sur les operations dans les ensembles abstracits et leur application aux equations integrales, Fund. Math., 3 (1922), 133-181.
• [6] R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76.
• [7] S. Reich, Fixed point of contractive functions, Boll. Unione Mat. Ital., 5 (1972), 26-42.
• [8] L. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. (Beograd)(NS), 12 (1971), 19-26.
• [9] S. Reich, Some remarks concerning contraction mappings, Canadian Mathematical Bulletin, 14 (1971), 121–124.
• [10] L.B, Ciric, On contraction type mappings, Math. Balk., 1 (1971), 52-57.
• [11] L.B, Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. (Belgr.), 12 (1971), 19-26.
• [12] S. Reich, Kannan’s fixed point theorem, Boll. Unione Mat. Ital., 4 (1971), 1–11.
• [13] I.A. Rus, Principles and applications of the fixed point theory, Editura Dacia, Clui-Napoca, Romania, (1979).
• [14] I.A. Rus, Generalized contractions and applications; Cluj University Press: Clui-Napoca, Romania, (2001).
• [15] H. A. Hançer, G. Mınak, I. Altun, On a broad category of multivalued weakly Picard operators, Fixed point theory, 18 (2017) 229-236.