Generalizations on contractive mappings in metric spaces

  • N. B. Okelo School of Mathematics and Actuarial Science, Jaramogi Oginga Odinga University of Science and Technology, P. O. Box 210-40601, Bondo
  • P. O. Mogotu Department of Mathematics, KISII University P. O. BOX 408-40200, KISII
  • Sabasi Omaoro Department of Mathematics, KISII University P. O. BOX 408-40200, KISII
Keywords: 1 Metric space, Fuzzy sets and Contractions

Abstract

We present new results on generalizations on metric spaces. New results are given on contractions in metric spaces and their fuzzy sets.

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References

Czerwik, S, Nonlinear set valued contraction mappings in b-metric spaces, Atti Sem Math. Univ. Modena, 46(1998), 263-276.

S L Singh, B. Prasad, Some coincidence theorems and stability of iterative procedures, Comput. Math. Appl. 55 (2008), 2512-2520.

Berinde, V, Generalized contractions in quasimetric spaces, Seminar on fixed point theory, Preprint no. 3(1993), 3-9.

Czerwik, S, Contraction mappings in b-metric spaces. Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.

S. L. Singh, S. Czerwik, Krzysztof Krol and Abha Singh, Coincidences and Fixed points of hybrid contractions, Tamsui Oxford Journal of Mathematical Sciences 24 (4) (2008) 401-416.

S. Heilpern, Fuzzy mappings and fixed point theorems, J. Math. Anal. Appl. 83 (1981) 566-569.

I. Beg, M. A. Ahmed, Common fixed point theorem for generalized fuzzy contraction mappings satisfying an implicit relation, Applied Mathematics Letters, In Press, Available online 17 December 2011.

M. Akkouchi, A common fixed point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces, Acta Univ. Palacki. Olomuc., Mathematica 50, 1 (2011) 5-15.

M. Akkouchi, Common Fixed Point Theorems for Two Self-mappings of a b-metric Space under an Implicit Relations, Hacettepe Journal of Mathematics and Statistics, Vol. 40 (6) (2011), 805-810.

S. L. Singh, B. Prasad, Some coincidence theorems and stability of iterative procedures, Computers and Mathematics with Applications 55 (2008) 2512-2520.

S. Czerwik, Contraction mappings in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis, Vol. 1 (1993), No. 1, 5—11.

M. Boriceanu, M. Bota, A. Petrusel, Multivalued fractals in b-metric spaces, Central European Journal of Mathematics, 8(2), 2010, 367-377.

S. B. Nadler, Multivalued contraction mappings, Pacific J. of Math., 1969, 30, 475-488.

V. Berinde, Sequences of operators and fixed points in quasimetric spaces, stud. Univ. “Babes-Bolyaiâ€, Math., 16(4)(1996), 23-27.

S. C. Arora, V. Sharma, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems 110 (2000) 127-130.

I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal. 30(1989), 26-37.

M. Bota, A. Molnar, C. Varga, On Ekeland`s variational principle in b-metric spaces, Fixed Point Theory, 12(2011), No. 2, 21-28.

Hussain, N, Roshan, JR, Parnaveh, V, Abbas, M,:Common fixed point results for weak contractive mappings in ordered b-dislocated metric spaces with applications, Journal of Inequalities and Applications 2013, 486(2013).

I. Beg, M. A. Ahmed, Common fixed point theorem for generalized fuzzy contraction mappings satisfying an implicit relation, Mat. Vesnik, Available online 20.04.2013.

Hitzler, P, Seda, AK: Dislocated topologies. J. Electr. Eng. 51(12), 3-7 (2000).

A. Isufati, I. Vardhami, K. Gjino, Fuzzy mappings in b-metric spaces, Proceddings of ICBWM 2013.

Published
2015-07-22
How to Cite
Okelo, N., Mogotu, P., & Omaoro, S. (2015). Generalizations on contractive mappings in metric spaces. Journal of Advanced Mathematics, 1(1), 01-03. Retrieved from https://asdpub.com/index.php/jam/article/view/73
Issue
Vol 1 No 1 (2015): JAM
Section
Original Articles

Copyright (c) 2015 Journal of Advanced Mathematics

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