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Strong coupled fixed points of Chatterjea type (psi ;phi)-weakly cyclic coupled mappings in S-metric spaces

Year 2020, Volume: 2 Issue: 1, 60 - 78, 30.06.2020

Abstract

In this paper, we introduce Chatterjea type (psi ;phi)-weakly cyclic coupled mapping in S-metric spaces and prove the existence and uniqueness of strong coupled fixed point of such mapping. We give an illustrative example in support of our result.

References

  • [1] Ajay Singh and Nawneet Hooda, Coupled fixed point theorems in S-metric spaces, IJMSI, 2 (4) (2014) 33-39.
  • [2] Ya. I. Alber, S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, New results in Operator Theory, Advances Appl., 8, (I. Gohberg and Yu. Lyubich, eds.), Birkhauser, Basel, (1997) 7-22.
  • [3] M. Almahalebi, A. H. Ansari, and S. Chandok, Fixed point theorem for cyclic (µ, ψ, ϕ)-weakly contractions via a new function, Analele Universitatii de Vest, Timsoara - Seria Matematica Informatica LV, 2 (2017) 3-15.
  • [4] G. V. R. Babu, Leta Bekere Kumssa, Fixed Points of (α, ψ, ϕ)- Generalized Weakly Contractive Maps and Property (P) in S-metric spaces, Filomat, 31 (14) (2017) 4469-4481.
  • [5] G. V. R. Babu, K. K. M. Sarma, V. A. Kumari and P. Sudheer Kumar, Fixed point results of various cyclic contractions in metric spaces, International Journal of Advances in Mathematics, 2018 (5) (2018) 1-13.
  • [6] G. V. R. Babu, P. D. Sailaja, G. Srichandana, Common fixed points via Ck-class functions in S-metric spaces, Journal of Fixed Point Theory, 2020 (1) (2020) pages 22.
  • [7] S. Chandok and M. Postolache, Fixed point theorem for weakly Chatterjea-type cyclic contractions, Fixed Point Theory and Applications, 2013 (28) (2013) 9 pages.
  • [8] S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci., (25) (1972) 727-730.
  • [9] B. S. Choudhury, Unique fixed point theorem for weak C-contractive mappings, kathmandu University Journal of Science, Engineering and Technology, 5 (1) (2009) 6-13.
  • [10] B. S. Choudhury and P. Maity, P. Konar, Fixed point results for coupling on metric spaces, U. P. B. Sci. Bull., series A, 79 (1) (2017) 77-88.
  • [11] T. Dosenovic, S. Radenovic, A. Rezvani and S. Sedghi, Coincidence Point Theorems in SMetric Spaces Using Inegral Type of Contraction, U. P. B. Sci. Bull, Series A, 79 (4) (2017) 145-158.
  • [12] N. V. Dung, On coupled common fixed points for mixed weakly monotone maps in partially ordered S-metric spaces, Fixed Point Theory and Appl., 2013 (48) (2013) 17 pages.
  • [13] N. V. Dung, N.T. Hieu and S.Radojevic, Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat, 28 (9) (2014) 1885-1898.
  • [14] T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006) 1379-1393.
  • [15] A. Gupta, Cyclic contraction on S-metric space, International Journal of Analysis and Applications, 3 (2013) 119-130.
  • [16] Hans Raj and Nawneet Hooda, Coupled coincidence fixed point theorems in S-metric spaces, IOSR Journal of Mathematics, 10 (2) (2014) 59-64.
  • [17] Hans Raj and Nawneet Hooda, Coupled fixed point theorems in S-metric spaces with mixed g-monotone property, IJETED, 4 (4) (2014) 68-81.
  • [18] H. Huang, G. Deng, T. Doˇsenovic, N. Hussain, Note on recent common coupled fixed point results in multiplicative metric spaces, Applied Mathematics and Nonlinear Sciences 3 (2) (2018) 659-668.
  • [19] M. M. Jaradat, Z. Mustafa, A. H. Ansari, P. S. Kumri, D. Dolicanin-Djekic and H. M. Jaradat, Some fixed point results for F α − W φ- generalized cyclic contractions on metric like space with applications to graphs and integral equations, J. Mat. Anal., 8 (1) (2017) 28-45.
  • [20] E. Karapinar, Fixed point theory for cyclic weak (φ, ϕ) contraction, Appl. Math. Lett., 24 (6) (2011) 822-825.
  • [21] E. Karapinar, and H. K. Nashine, Fixed point theorem for cyclic Chatterjea type contractions, Journal of Applied Mathematics, 2012 (2012) pages 15.
  • [22] E. Karapinar, A. Yildiz-Ulus, and I. M. Erhan, Cyclic contractions on G-metric spaces, Abstract and Applied Analysis, 2012 (2012) 15 pages.
  • [23] W. A. Kirk, P. S. Srinivasan and P. Veeramani, Fixed points for mapping satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003) 79-89.
  • [24] C. Klin-Eam and C. Suanoom, Dislocated quasi b-metric spaces and fixed point theorems for cyclic contractions, Fixed Point Theory and Appl., 74 (2015) 12 pages.
  • [25] R. Krishnakumar, T. Mani, D. Dhamodharan, Coupled common fixed point theorems of C-class function on ordered S-metric spaces, 6 (2) (2019) 184-192.
  • [26] P. S. Kumari and D. Panthi, Cyclic compatible contraction and related fixed point theorems, Fixed Point Theory and Appl., 28 (2016) 18 pages.
  • [27] P. S. Kumari and D. Panthi, Connecting various types of cyclic contractions and contractive self-mapping with Hardy-Rogers self-mappings, Fixed Point Theory and Appl., 15 (2016) 19 pages.
  • [28] V. LakshmiKantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (12) (2009) 4341-4349.
  • [29] B. Nurwahyu, Fixed point theorems for cyclic weakly contraction mappings in dislocated Quasi extended -b metric Space, Journal of function spaces, 2019 (2019) 10 pages.
  • [30] M. Pacurar, and I. A. Rus, Fixed point theory for cyclic ϕ-contractions, Nonlinear Anal., 72 (2010) 1181-1187.
  • [31] T. Phaneendra, K. Kumara Swamy, Fixed points of Chatterjee and Ciric contractions on an S-metric space, IJPAM, 115 (2) (2017) 316-367.
  • [32] E. Prajisha and P. S. Shaini, Coupled fixed point theorems in partially ordered sets, Journal Nonlinear Analysis and Application, 2018 (2) (2018) 76-82.
  • [33] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001) 2683-2693.
  • [34] I. A. Rus, Cyclic representation and fixed points, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 3 (2005) 171-178.
  • [35] S. Sedghi, N. Shobe and A. Alouche, A generalization of fixed point theorem in S-metric spaces, Math. Vesnik, 64 (3) (2012) 258-266.
  • [36] S. Sedghi and N. V. Dung, Fixed point theorems on S-metric spaces, Math. Vesnik, 66 (1) (2014) 113-124.
  • [37] M. Zhou and X. L. Liu, On coupled common fixed point theorems for Geraghty-type contraction mappings using mixed weakly monotone property in partially ordered S-metric spaces, J. Funct. Spaces, 2016 (2016) 9 pages.
Year 2020, Volume: 2 Issue: 1, 60 - 78, 30.06.2020

Abstract

References

  • [1] Ajay Singh and Nawneet Hooda, Coupled fixed point theorems in S-metric spaces, IJMSI, 2 (4) (2014) 33-39.
  • [2] Ya. I. Alber, S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, New results in Operator Theory, Advances Appl., 8, (I. Gohberg and Yu. Lyubich, eds.), Birkhauser, Basel, (1997) 7-22.
  • [3] M. Almahalebi, A. H. Ansari, and S. Chandok, Fixed point theorem for cyclic (µ, ψ, ϕ)-weakly contractions via a new function, Analele Universitatii de Vest, Timsoara - Seria Matematica Informatica LV, 2 (2017) 3-15.
  • [4] G. V. R. Babu, Leta Bekere Kumssa, Fixed Points of (α, ψ, ϕ)- Generalized Weakly Contractive Maps and Property (P) in S-metric spaces, Filomat, 31 (14) (2017) 4469-4481.
  • [5] G. V. R. Babu, K. K. M. Sarma, V. A. Kumari and P. Sudheer Kumar, Fixed point results of various cyclic contractions in metric spaces, International Journal of Advances in Mathematics, 2018 (5) (2018) 1-13.
  • [6] G. V. R. Babu, P. D. Sailaja, G. Srichandana, Common fixed points via Ck-class functions in S-metric spaces, Journal of Fixed Point Theory, 2020 (1) (2020) pages 22.
  • [7] S. Chandok and M. Postolache, Fixed point theorem for weakly Chatterjea-type cyclic contractions, Fixed Point Theory and Applications, 2013 (28) (2013) 9 pages.
  • [8] S. K. Chatterjea, Fixed-point theorems, C. R. Acad. Bulgare Sci., (25) (1972) 727-730.
  • [9] B. S. Choudhury, Unique fixed point theorem for weak C-contractive mappings, kathmandu University Journal of Science, Engineering and Technology, 5 (1) (2009) 6-13.
  • [10] B. S. Choudhury and P. Maity, P. Konar, Fixed point results for coupling on metric spaces, U. P. B. Sci. Bull., series A, 79 (1) (2017) 77-88.
  • [11] T. Dosenovic, S. Radenovic, A. Rezvani and S. Sedghi, Coincidence Point Theorems in SMetric Spaces Using Inegral Type of Contraction, U. P. B. Sci. Bull, Series A, 79 (4) (2017) 145-158.
  • [12] N. V. Dung, On coupled common fixed points for mixed weakly monotone maps in partially ordered S-metric spaces, Fixed Point Theory and Appl., 2013 (48) (2013) 17 pages.
  • [13] N. V. Dung, N.T. Hieu and S.Radojevic, Fixed point theorems for g-monotone maps on partially ordered S-metric spaces, Filomat, 28 (9) (2014) 1885-1898.
  • [14] T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006) 1379-1393.
  • [15] A. Gupta, Cyclic contraction on S-metric space, International Journal of Analysis and Applications, 3 (2013) 119-130.
  • [16] Hans Raj and Nawneet Hooda, Coupled coincidence fixed point theorems in S-metric spaces, IOSR Journal of Mathematics, 10 (2) (2014) 59-64.
  • [17] Hans Raj and Nawneet Hooda, Coupled fixed point theorems in S-metric spaces with mixed g-monotone property, IJETED, 4 (4) (2014) 68-81.
  • [18] H. Huang, G. Deng, T. Doˇsenovic, N. Hussain, Note on recent common coupled fixed point results in multiplicative metric spaces, Applied Mathematics and Nonlinear Sciences 3 (2) (2018) 659-668.
  • [19] M. M. Jaradat, Z. Mustafa, A. H. Ansari, P. S. Kumri, D. Dolicanin-Djekic and H. M. Jaradat, Some fixed point results for F α − W φ- generalized cyclic contractions on metric like space with applications to graphs and integral equations, J. Mat. Anal., 8 (1) (2017) 28-45.
  • [20] E. Karapinar, Fixed point theory for cyclic weak (φ, ϕ) contraction, Appl. Math. Lett., 24 (6) (2011) 822-825.
  • [21] E. Karapinar, and H. K. Nashine, Fixed point theorem for cyclic Chatterjea type contractions, Journal of Applied Mathematics, 2012 (2012) pages 15.
  • [22] E. Karapinar, A. Yildiz-Ulus, and I. M. Erhan, Cyclic contractions on G-metric spaces, Abstract and Applied Analysis, 2012 (2012) 15 pages.
  • [23] W. A. Kirk, P. S. Srinivasan and P. Veeramani, Fixed points for mapping satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003) 79-89.
  • [24] C. Klin-Eam and C. Suanoom, Dislocated quasi b-metric spaces and fixed point theorems for cyclic contractions, Fixed Point Theory and Appl., 74 (2015) 12 pages.
  • [25] R. Krishnakumar, T. Mani, D. Dhamodharan, Coupled common fixed point theorems of C-class function on ordered S-metric spaces, 6 (2) (2019) 184-192.
  • [26] P. S. Kumari and D. Panthi, Cyclic compatible contraction and related fixed point theorems, Fixed Point Theory and Appl., 28 (2016) 18 pages.
  • [27] P. S. Kumari and D. Panthi, Connecting various types of cyclic contractions and contractive self-mapping with Hardy-Rogers self-mappings, Fixed Point Theory and Appl., 15 (2016) 19 pages.
  • [28] V. LakshmiKantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (12) (2009) 4341-4349.
  • [29] B. Nurwahyu, Fixed point theorems for cyclic weakly contraction mappings in dislocated Quasi extended -b metric Space, Journal of function spaces, 2019 (2019) 10 pages.
  • [30] M. Pacurar, and I. A. Rus, Fixed point theory for cyclic ϕ-contractions, Nonlinear Anal., 72 (2010) 1181-1187.
  • [31] T. Phaneendra, K. Kumara Swamy, Fixed points of Chatterjee and Ciric contractions on an S-metric space, IJPAM, 115 (2) (2017) 316-367.
  • [32] E. Prajisha and P. S. Shaini, Coupled fixed point theorems in partially ordered sets, Journal Nonlinear Analysis and Application, 2018 (2) (2018) 76-82.
  • [33] B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001) 2683-2693.
  • [34] I. A. Rus, Cyclic representation and fixed points, Annals of the Tiberiu Popoviciu Seminar of Functional Equations, Approximation and Convexity, 3 (2005) 171-178.
  • [35] S. Sedghi, N. Shobe and A. Alouche, A generalization of fixed point theorem in S-metric spaces, Math. Vesnik, 64 (3) (2012) 258-266.
  • [36] S. Sedghi and N. V. Dung, Fixed point theorems on S-metric spaces, Math. Vesnik, 66 (1) (2014) 113-124.
  • [37] M. Zhou and X. L. Liu, On coupled common fixed point theorems for Geraghty-type contraction mappings using mixed weakly monotone property in partially ordered S-metric spaces, J. Funct. Spaces, 2016 (2016) 9 pages.
There are 37 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Articles
Authors

G. V. R. Babu 0000-0002-6272-2645

Pericherla Durga Saılaja 0000-0002-2309-8851

Gadhavajjala Srıchandana 0000-0001-7443-8214

Publication Date June 30, 2020
Acceptance Date June 29, 2020
Published in Issue Year 2020 Volume: 2 Issue: 1

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