Families of mappings satisfying a mixed implicit relation

Rajesh Kumar, Sanjay Kumar

Abstract


A fixed point for a suitable map or operator is identical to the presence of a solution to a theoretical or real-world problem. As a result, fixed points are crucial in many fields of mathematics, science and engineering. The purpose of this paper is to prove unique common fixed point theorems for families of weakly compatible mappings. Given mappings satisfy common limit range property and a mixed implicit relation. Our results generalize, extend and improve the results of Imdad (2013) and Popa (2018). We provide an application for integral type contraction condition. An example is also mentioned to check the authenticity of our results.


Keywords


common fixed point, weakly compatible mappings, mixed implicit relation, almost altering distance, common limit range propperty

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References


A. Aamri, D. El-Moutawakil, "Some new common fixed point theorems under strict contractive conditions," Math. Anal. Appl. 270 (2002), 181-188.

J. Ali, M. Imdad, "An implicit function implies several contractive conditions," Sarajevo J. Math., 17 (2008), 269–285.

Ya.I. Alber, S. Guerre-Delabrierre, "Principle of weakly contractive maps in Hilbert spaces," In: New Results in Operator Theory and its Applications, Adv. Appl. Math. 98 (Y. Gahbery, Yu. Librich, eds.), Birkhauser Verlag Basel, 1997, pp. 7–22.

A. Branciari, "A fixed point theorem for mappings satisfying a general contractive condition of integral type," Int. J. Math. Math. Sci. 29(9) (2002), 531-536.

D. W. Boyd and T. S. W. Wong, "On nonlinear contractions," Proceedings of the American Mathematical Society, vol. 20, no. 2, pp. 458–464, 1969.

S. Banach, "Sur les opérations dans les ensembles abstraits et leurs applications," Fundam. Math. 3 (1922), 133-181.

M. Imdad, S. Chauhan, "Employing common limit range property to prove unified metrical common fixed point theorems," Intern. J. Anal. 2013, Article ID 763261.

M. Imdad, S. Chauhan, Z. Kadelburg, "Fixed point theorems for mappings with common limit range property satisfying generalized (ψ, ϕ)-weak contractive conditions," Math. Sci. 7 (2013), DOI: 10.1186/2251-7456-7-16.

G. Jungck, "Commuting mappings and fixed points," Amer. Math. Monthly 83 (1976), 261-263.

G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Math. Sci. 9(4)(1986), 771-779.

G. Jungck, Common fixed points for noncommuting nonself mappings on nonnumeric spaces, Far East J. Math. Sci. 4 (1996), 195–215.

M.S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distance between two points, Bull. Austral. Math. Soc. 30 (1984), 1-9.

R.P. Pant, Common fixed points for contractive maps, J. Math. Anal. Appl. 226 (1998), 251–258.

R.P. Pant, R-weak commutativity and common fixed points of noncompatible maps, Ganita 99 (1999), 19–26.

R.P. Pant, R-weak commutativity and common fixed points, Soochow J. Math. 25 (1999), 39–42.

R.P. Pant, A common fixed point theorems under a new condition, Indian J. Pure Appl. Math., 30(20) (1999), 147-152

V. Popa and A.M. Patriciu, A general fixed point theorem for two pairs of mappings satisfying a mixed implicit relation, Mathematica Slovaca, 68 No.3 (2018), 655-666.

V. Popa, A.M. Patriciu, A general fixed point theorem for a pair of self mappings with common limit range property in G-metric spaces, Facta Univ. Ser. Math. Inform. 29(4)(2014), 351-370.

V. Popa, M. Mocanu, Altering distance and common fixed points under implicit relations, Hacet. J. Math. Stat. 38(3)(2009), 329-337.

V. Popa, A general fixed point theorem for weakly subsequentially continuous mappings, Fasciculi Mathematici, 62(2019), 103-119.

B.E. Rhoades, Some theorems of weakly contractive maps, Nonlinear Anal., 47(2001), 2683-2693.

W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. (2011), Article ID 637958.




DOI: http://dx.doi.org/10.23755/rm.v47i0.839

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