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Some Fixed Point Theorems for Weak Compatible Mappings in G-Metric Spaces

Year 2017, , 16 - 28, 25.08.2017
https://doi.org/10.17780/ksujes.322349

Abstract

In this work it
was given  the existence of the unique
common fixed point theorems for weakly compatible mappings and results.in
 -metric
spaces.

References

  • Kaewcharoen A., Yuying T., (2014). Unique common fixed point theorems on partial metric spaces, J. of nonlinear Sci. and Appl. , 7, 90-101.
  • Banach, S., (1922). Surles operations dansles ensembles abstracits et leur application aux equations integrales, Fund Math. 000003,133-181.
  • Kannan, R., , (1968). Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76.
  • Reich, S., (1971). Some remarks concerning contraction mappings. Can. Math. Bull. 14, 121-124.
  • Chatterjea, S. K., (1972). Fixed point theorems. C. R. Acad. Bulg. Sci. 25, 727-730.
  • Zamfirescu T., (1972). Fixed point theorems in metric spaces, Arch. Math. (Basel) 23, 292-298.
  • Hardy G. E., Rogers, T.D., (1973). A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16, 201-206.
  • Alber, Ya. I., Guerre-Delabriere, S., (1997). Principles of weakly contractive maps in Hilbert Spaces, in: I. Gohberg, Yu. Lyubich (Eds.), New Results in Operator Theory, in: Advences and Appl., 7-22, 98.
  • Rhoades, B. E., (2001). Some theorems on weakly contractive maps, Nonlinear Anal. 47, (4), 2683-2693.
  • Dutta, P. N., Choudhury, B. S., (2008). A generalization of contraction principle in metric spaces. Fixed point Theory and Applications Article, I. D., 8, 406368.
  • Popescu, O., (2011). Fixed points for ψ,φ- weak contractions. Appl. Math. Lett. , 1-4, 24.
  • Berinde, V., (2008). General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J., 24, no. 2, 10-19.
  • Berinde, V., (2003). On the approximatation of weak contractive mappings. Carpathian J. Math. 19, (1), 7-22.
  • Berinde, V., (2007). Approximatating of fixed points. Springer- Verlag. Berlin-Heidelberg.
  • Berinde, V., (2004). Approximatating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9, (1), 43-57.
  • Mustafa, Z., Sims, B., (2006). A new approach to a generalized metric spaces. J. Nonlinear Convex Anal., 7 (2), 289-297.
  • Jungck, G., (1976). Commuting Mappings and Fixed Points, Amer. Math. Monthly, 83: 261-263.
  • Jungck, G., Rhoades, B. E., (1998). Fixed Point for Set Valued Functionons without Continuity, Indian J., Pure Applied Math., 29 (3), 227-238.
  • Abbas, M. Babu G.V.R. and Alemayehu, G.N. (2011). On common fixed points of weakly compatible mappings satisfying generalized condition, Filomat., 25, 9-19.
  • Sushil Sharma , Bhavana Deshpande , and Alok Pandey, (2011). Common fixed point theorem for a pair of weakly compatible mappings on Banach spaces, East Asian Math. J. 27, (5), 573-583.
  • Suzuki, T. (2007). Meir-Keeler contractions of integral type are still Meir-Keeler contractions. Internat. J. Math. Math. Sci., Article ID 39281, 6 pages, MR2285999 (2007k:54049).
  • Vetro, C. (2010). On Branciari’s theorem for weakly compatible mappings. Appl. Math. Lett., MR2609801 (2011 d: 47136)., 23, (6), 700–705.

G-Metrik Uzayda Zayıf Uyumlu Dönüşümler İçin Bazı Sabit Nokta Teoremleri

Year 2017, , 16 - 28, 25.08.2017
https://doi.org/10.17780/ksujes.322349

Abstract

Bu çalışmada, G-metrik uzayda zayıf
uyumlu dönüşümler için bazı sabit nokta teoremleri ve sonuçlar verildi.

References

  • Kaewcharoen A., Yuying T., (2014). Unique common fixed point theorems on partial metric spaces, J. of nonlinear Sci. and Appl. , 7, 90-101.
  • Banach, S., (1922). Surles operations dansles ensembles abstracits et leur application aux equations integrales, Fund Math. 000003,133-181.
  • Kannan, R., , (1968). Some results on fixed points. Bull. Calcutta Math. Soc. 60, 71-76.
  • Reich, S., (1971). Some remarks concerning contraction mappings. Can. Math. Bull. 14, 121-124.
  • Chatterjea, S. K., (1972). Fixed point theorems. C. R. Acad. Bulg. Sci. 25, 727-730.
  • Zamfirescu T., (1972). Fixed point theorems in metric spaces, Arch. Math. (Basel) 23, 292-298.
  • Hardy G. E., Rogers, T.D., (1973). A generalization of a fixed point theorem of Reich, Canad. Math. Bull. 16, 201-206.
  • Alber, Ya. I., Guerre-Delabriere, S., (1997). Principles of weakly contractive maps in Hilbert Spaces, in: I. Gohberg, Yu. Lyubich (Eds.), New Results in Operator Theory, in: Advences and Appl., 7-22, 98.
  • Rhoades, B. E., (2001). Some theorems on weakly contractive maps, Nonlinear Anal. 47, (4), 2683-2693.
  • Dutta, P. N., Choudhury, B. S., (2008). A generalization of contraction principle in metric spaces. Fixed point Theory and Applications Article, I. D., 8, 406368.
  • Popescu, O., (2011). Fixed points for ψ,φ- weak contractions. Appl. Math. Lett. , 1-4, 24.
  • Berinde, V., (2008). General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian J., 24, no. 2, 10-19.
  • Berinde, V., (2003). On the approximatation of weak contractive mappings. Carpathian J. Math. 19, (1), 7-22.
  • Berinde, V., (2007). Approximatating of fixed points. Springer- Verlag. Berlin-Heidelberg.
  • Berinde, V., (2004). Approximatating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9, (1), 43-57.
  • Mustafa, Z., Sims, B., (2006). A new approach to a generalized metric spaces. J. Nonlinear Convex Anal., 7 (2), 289-297.
  • Jungck, G., (1976). Commuting Mappings and Fixed Points, Amer. Math. Monthly, 83: 261-263.
  • Jungck, G., Rhoades, B. E., (1998). Fixed Point for Set Valued Functionons without Continuity, Indian J., Pure Applied Math., 29 (3), 227-238.
  • Abbas, M. Babu G.V.R. and Alemayehu, G.N. (2011). On common fixed points of weakly compatible mappings satisfying generalized condition, Filomat., 25, 9-19.
  • Sushil Sharma , Bhavana Deshpande , and Alok Pandey, (2011). Common fixed point theorem for a pair of weakly compatible mappings on Banach spaces, East Asian Math. J. 27, (5), 573-583.
  • Suzuki, T. (2007). Meir-Keeler contractions of integral type are still Meir-Keeler contractions. Internat. J. Math. Math. Sci., Article ID 39281, 6 pages, MR2285999 (2007k:54049).
  • Vetro, C. (2010). On Branciari’s theorem for weakly compatible mappings. Appl. Math. Lett., MR2609801 (2011 d: 47136)., 23, (6), 700–705.
There are 22 citations in total.

Details

Subjects Engineering
Journal Section Research Articles
Authors

Cafer Aydın

Seher Sultan Sepet

Publication Date August 25, 2017
Submission Date June 19, 2017
Published in Issue Year 2017

Cite

APA Aydın, C., & Sepet, S. S. (2017). G-Metrik Uzayda Zayıf Uyumlu Dönüşümler İçin Bazı Sabit Nokta Teoremleri. Kahramanmaraş Sütçü İmam Üniversitesi Mühendislik Bilimleri Dergisi, 20(2), 16-28. https://doi.org/10.17780/ksujes.322349