Multi-valued tripled fixed point results via CLR property in metric spaces with application

Authors

Muhammad Shoaib - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
Muhammad Sarwar - Department of Mathematics, University of Malakand, Chakdara Dir(L), Pakistan.
Yongjin Li - Department of Mathematics Sun Yat-sen University, Guangzhou, Guangdong, China

Abstract

In this work, using CLR property, tripled coincidence and common fixed point theorems for hybrid pair of mappings are studied. As an application, existence of solution to the system of integral equation is also discussed.

Keywords

Hybrid maps, tripled fixed point, CLR property

References

[1] A. A. N. Abdou, Common fixed point results for multi-valued mappings with some examples, J. Nonlinear Sci. Appl., 9 (2016), 787–798.
[2] Y. I. Alber, S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, New results in operator theory and its applications, Oper. Theory Adv. Appl., Birkhäuser, Basel, 98 (1997), 7–22.
[3] A. Amini-harandi, D. O’Regan, On coupled and tripled fixed point theory of multi-valued contraction mappings in partially ordered metric spaces, Commun. Appl. Anal., 19 (2015), 209–216.
[4] H. Aydi, M. Abbas, Tripled coincidence and fixed point results in partial metric spaces, Appl. Gen. Topol., 13 (2012), 193–206.
[5] V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889–4897.
[6] B. Deshpande, C. Kothari, A. Handa, Common tripled fixed point theorems under weaker conditions, Int. J. Pure Appl. Math., 103 (2015), 1–17.
[7] B. Deshpande, S. Sharma, A. Handa, Tripled fixed point theorem for hybrid pair of mappings under generalized nonlinear contraction, J. Korean Soc. Math. Educ. Ser. B Pure Appl. Math., 21 (2014), 23–38.
[8] D. Doric, Common fixed point for generalized (\(\psi,\phi\))-weak contractions, Appl. Math. Lett., 22 (2009), 1896–1900.
[9] P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 8 pages.
[10] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379–1393.
[11] J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188–1197.
[12] M. A. Khan, Sumitra, CLRg property for coupled xed point theorems in fuzzy metric spaces, Int. J. Appl. Phys. Math., 2 (2012), 355–358.
[13] V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341–4349.
[14] S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math., 20 (1969), 475–488.
[15] K. P. R. Rao, G. N. V. Kishore, K. Tas, A unique common triple fixed point theorem for hybrid pair of maps, Abstr. Appl. Anal., 2012 (2012), 9 pages.
[16] K. P. R. Rao, K. V. Siva Parvathi, M. Imdad, hybrid coupled fixed point theorems for maps under (CLRg) property in fuzzy metric spaces, Novi Sad J. Math., (2015), 18 pages.
[17] K. P. R. Rao, A. Sombabu, M. Mustaq Ali, Common coupled fixed point theorems satisfying (CLRg) property in complex valued b-metric spaces, Bull. Int. Math. Virtual Inst., 6 (2016), 189–198.
[18] B. E. Rhoades, Some theorems on weakly contractive maps, Proceedings of the Third World Congress of Nonlinear Analysts, Part 4, Catania, (2000), Nonlinear Anal., 47 (2001), 2683–2693.
[19] B. Samet, C. Vetro, Coupled fixed point, F-invariant set and fixed point of N-order, Ann. Funct. Anal., 1 (2010), 46–56.
[20] W. Shatanawi, M. Postolache, Z. Mustafa, Tripled and coincidence fixed point theorems for contractive mappings satisfying \(\Phi\)-maps in partially ordered metric spaces, An. Ştiinţ. Univ. ”Ovidius” Constanţa Ser. Mat., 22 (2014), 179–203.
[21] W. Sintunavarat, P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., 2011 (2011), 14 pages.
[22] Q.-N. Zhang, Y.-S. Song, Fixed point theory for generalized \(\phi\)-weak contractions, Appl. Math. Lett., 22 (2009), 75–78.

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