Volume 68 | Issue 6 | Year 2022 | Article Id. IJMTT-V68I6P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V68I6P513
Received | Revised | Accepted | Published |
---|---|---|---|
23 Apr 2022 | 07 Jun 2022 | 18 Jun 2022 | 28 Jun 2022 |
In this paper, we have proved the existence and uniqueness of common fixed point theorems for complete metric space. Our results generalizes fixed point results in existing literature.
[1] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations integrals, Fundamental Mathematicae. 3 (1922) 133-181.
[2] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60(1968) 71-76.
[3] D. N. Sarkhel, Banach’s fixed point theorem implies Kannan’s, bull. Cal. Mayh. Soc. 91(2) (1999) 143-144.
[4] S. K. Chatterjea, Fixed point theorem, C.R. Acad. Bulgare Sci. 25 (1972) 727-730.
[5] J. R. Jaroslaw, Fixed point theorems for Kannan type mappings, J. Fixed point theory Appl. (2017).
[6] G. Dhananjay, K. Poom and A. Mujahid, Background and recent developments of Metric Fixed Point Theory, CRC press, Taylor and Francis Group, (2018).
[7] V. Subrahmanyam, Completeness and fixed points, Monatsh. Math. 80(1975) 325-330.
[8] S. Reich, Kannan’s fixed point theore,. Boll. Un. Mat. Ital. 4(4) (1971) 1-11.
[9] T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl. 253(2001) 440-458.
[10] T. Suzuki and W. Takahashi, Fixed point theorems and charactrizations of metric completeness, Topol. Methods Nonlinear Anal. 8(1996) 371-382.
[11] L. B. Ciric, Fixed point theorems for multi-valued contractions in complete metric spaces, J. Math. Anal. Appl. 348(2008) 499- 507.
[12] G. F. Simmons, Introduction to Topology and Modern Analysis, R.E. Krieger publishing Company, (1983).
[13] C. T. Aage, J. N. Salunke, The results on fixed points in dislocated and dislocated quasi-metric space, Applied Math. Sci., 2(59) (2008), 2941-2948.
[14] G. E. Hardy and T. D. Rogers, A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16(2)1971, 201- 206.
[15] S. B. Nadler, Sequences of contractions and fixed points, Pacific J. Math. 27(1968), 579-585.
[16] F. F. Bonsall, Lectures on some fixed point theorems of functional analysis, Tata Institute of Fundamental Research, Bombay, 1952.
[17] E. Rakotch, A note on contractive mappings, Proc. Amer. Math. Soc. 13(1962), 459-465.
[18] Meir and E. Keeler, A theorem on contractive mappings, J. Math. Anal. Appl. 28(1969), 26-29.
[19] U. P. Dolhare and V. V. Nalawade, Generalizations of Banach contraction mapping principle, American Inter. J. of Research in Sci. Tech. Engi.& Maths. 26(1) (2019), 98-106.
[20] R. Kannan, Some results on fixed points-II, Amer. Math. Monthly, 76(1969), 405-408.
[21] P. V. Subrahmanyam, Completeness and fixed points, Monatshefte Math. 80(1975), 325-330.
[22] J. S. Ume, Fixed point theorems for Kannan-type maps, Fixed point Theory and Applications, 38(2015), 1-13.
[23] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Ana. 47(2001), 2683-2693.
[24] R. Shrivastava, R. Kumar Dubey and P. Tiwari, Common fixed point theorem in complete metric space, Advances and Applied Science Research, 4(6) (2013), 82-89.
[25] P. N. Datta and B. S. Chaudhary, A generalization of contraction principle in metric space, Fixed Point Throe. Appl.(2008)
Godavari Jojar, Uttam Dolhare, Sachin Basude, Nitin Darkunde, Prashant Swam, "Some Results on Unique Fixed Point Theorems in Complete Metric Space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 68, no. 6, pp. 111-116, 2022. Crossref, https://doi.org/10.14445/22315373/IJMTT-V68I6P513