Research Article

FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES

Volume: 41 Number: 2 February 1, 2012
  • Hemant Kumar Nashine
  • İshak Altun
EN

FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES

Abstract

Fixed point theorems for a pair of mappings which satisfy the condition of being generalized weakly contractive in complete ordered metric spaces are derived. At the end of the paper, applications of the previous results to new fixed point results of integral type are also shown. 

Keywords

References

  1. Agarwal, R.P., El-Gebeily, M.A. and and O’Regan, D. Generalized contractions in partially ordered metric spaces, Applicable Analysis 87 (1), 109–116, 2008.
  2. Alber, Ya.E. and Guerre-Delabriere, S. Principles of weakly contractive maps in Hilbert spaces, in: New Results in Operator Theory and its Applications (I.Gohberg and Yu. Lyubich, eds.) (Oper. Theory Adv. Appl. 98, Birkhauser, Basel, 1997), 7–22.
  3. Abbas, M. and Khan, M.A. Common fixed point theorem of two mappings satisfying a generalized weak contractive condition, Inter. J. Math. Math. Sci., Article ID 131068, 9 pages, 2009.
  4. Altun, I. and Simsek, H. Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory and Applications, Article ID 621492, 17 pages, 2010.
  5. Amini-Harandi, A. and Emami, H. A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Analysis 72 (5), 2238–2242, 2010.
  6. Beg, I. and Butt, A.R. —em Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Analysis 71 (9), 3699–3704, 2009.
  7. Beg, I. and Butt, A.R. Fixed points for weakly compatible mappings satisfying an implicit relation in partially ordered metric spaces, Carpathian Journal of Mathematics 25 (1), 1–12, 2009.
  8. Bhaskar, T.G. and Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (7), 1379–1393, 2006.

Details

Primary Language

English

Subjects

Statistics

Journal Section

Research Article

Authors

Hemant Kumar Nashine This is me

İshak Altun This is me

Publication Date

February 1, 2012

Submission Date

May 11, 2014

Acceptance Date

-

Published in Issue

Year 2012 Volume: 41 Number: 2

APA
Nashine, H. K., & Altun, İ. (2012). FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES. Hacettepe Journal of Mathematics and Statistics, 41(2), 243-253. https://izlik.org/JA96MP28PH
AMA
1.Nashine HK, Altun İ. FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES. Hacettepe Journal of Mathematics and Statistics. 2012;41(2):243-253. https://izlik.org/JA96MP28PH
Chicago
Nashine, Hemant Kumar, and İshak Altun. 2012. “FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES”. Hacettepe Journal of Mathematics and Statistics 41 (2): 243-53. https://izlik.org/JA96MP28PH.
EndNote
Nashine HK, Altun İ (February 1, 2012) FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES. Hacettepe Journal of Mathematics and Statistics 41 2 243–253.
IEEE
[1]H. K. Nashine and İ. Altun, “FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES”, Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, pp. 243–253, Feb. 2012, [Online]. Available: https://izlik.org/JA96MP28PH
ISNAD
Nashine, Hemant Kumar - Altun, İshak. “FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES”. Hacettepe Journal of Mathematics and Statistics 41/2 (February 1, 2012): 243-253. https://izlik.org/JA96MP28PH.
JAMA
1.Nashine HK, Altun İ. FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES. Hacettepe Journal of Mathematics and Statistics. 2012;41:243–253.
MLA
Nashine, Hemant Kumar, and İshak Altun. “FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES”. Hacettepe Journal of Mathematics and Statistics, vol. 41, no. 2, Feb. 2012, pp. 243-5, https://izlik.org/JA96MP28PH.
Vancouver
1.Hemant Kumar Nashine, İshak Altun. FIXED POINT THEOREMS FOR A PAIR OF MAPPINGS SATISFYING A GENERALIZED WEAKLY CONTRACTIVE CONDITION IN ORDERED METRIC SPACES. Hacettepe Journal of Mathematics and Statistics [Internet]. 2012 Feb. 1;41(2):243-5. Available from: https://izlik.org/JA96MP28PH