### Common Fixed Point Theorems of Quadruple Mappings Satisfying \(CLR\) Property in \(G_p\) Metric Spaces With Applications

#### Abstract

The aim of this paper is to establish common fixed point theorems for quadruple of weakly compatible mappings satisfying a new type of common limit range property and involving almost altering distances in \(G_p\) metric space. Furthermore, we present an example to validate our main result. Further, we obtain some common fixed point theorems for mappings satisfying contractive conditions of integral type and for \(\varphi\)-contractive mappings.

#### Keywords

#### Full Text:

PDF#### References

M. Abbas and B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Applied Mathematics and Computation 215 (2009), 262 – 269, DOI: 10.1016/j.amc.2009.04.085.

M. R. Ahmadi Zand and A. Dehghan Nezhad, A generalization of partial metric spaces, Journal of Contemporary Applied Mathematics 1(1) (2011), 85 – 93, URL: https://www.researchgate.net/publication/284286285.

H. Aydi, E. Karapınar and P. Salimi, Some fixed point results in Gp-metric spaces, Journal of Applied Mathematics 2012 (2012), Art. ID 891713, 16 p., DOI: 10.1155/2012/891713.

M. A. Barakat and A. M. Zidan, A common fixed point theorem for weak contractive maps in Gp-metric spaces, Journal of the Egyptian Mathematical Society 23(2) (2015), 309 – 314, DOI: 10.1016/j.joems.2014.06.008.

N. Bilgili, E. Karapınar and P. Salimi, Fixed point theorems for generalized contractions on Gp-metric spaces, Journal of Inequalities and Applications 2013 (2013), Article number 39, DOI: 10.1186/1029-242X-2013-39.

A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences 29(9) (2002), 531 – 536, DOI: 10.1155/S0161171202007524.

G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly 83 (1976), 261 – 263, DOI: 10.1080/00029890.1976.11994093.

G. Jungck, Compatible mappings and common fixed points, International Journal of Mathematics and Mathematical Sciences 9 (1986), 771 – 779, DOI: 10.1155/S0161171286000935.

G. Jungck and B. E. Rhoades, Fixed points for set valued functions without continuity, Indian Journal of Pure Applied Mathematics 29 (1998), 227 – 238, https://insa.nic.in/writereaddata/UpLoadedFiles/IJPAM/20005a06_227.pdf.

M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society 30(1) (1984), 1 – 9, DOI: 10.1017/S0004972700001659.

J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proceedings of the American Mathematical Society 62(2) (1977), 344 – 348, DOI: 10.1090/S0002-9939-1977-0436113-5.

S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728 (1994), 183 – 197, DOI: 10.1111/j.1749-6632.1994.tb44144.x.

Z. Mustafa and B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear Convex Analysis 7(2) (2006), 289 – 297, http://www.ybook.co.jp/online2/jncav7.html.

Z. Mustafa and B. Sims, Some remarks concerning D-metric spaces, in International Conference on Fixed Point Theory and Applications, 189 – 198 (2003), URL: https://www.researchgate.net/publication/228569846.

V. Parvaneh, J. R. Roshan and Z. Kadelburg, On generalized weakly Gp-contractive mappings in ordered Gp-metric spaces, Gulf Journal of Mathematics 1(1) (2013), 78 – 97, https://gjom.org/index.php/gjom/article/view/241.

V. Popa, Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property, Filomat 31(11) (2017), 3181 – 3192, DOI: 10.2298/FIL1711181P.

V. Popa, Fixed points theorems for implicit contractive mappings, Studii si Cercetari Stiintifice. Seria: Matematica. Universitatea din Bacau 7 (1997), 127 – 133.

V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relations, Demonstratio Mathematica 32(1) (1999), 157 – 163, DOI: 10.1515/dema-1999-0117.

V. Popa and A.-M. Patriciu, A general fixed point theorem for a pair of self mappings with common limit range property in G-metric spaces, Facta Universitatis (Niš) Ser. Math. Inform. 29(4) (2014), 351 – 370, http://casopisi.junis.ni.ac.rs/index.php/FUMathInf/article/download/192/pdf.

V. Popa and A.-M. Patriciu, Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property in Gp metric spaces, Annales Mathematicae Silesianae 32 (2018), 295 – 312, DOI: 10.2478/amsil-2018-0002.

V. Popa and A.-M. Patriciu, Two general fixed point theorems for a sequence of mappings satisfying implicit relations in Gp-metric spaces, Applied General Topology 16(2) (2015), 225 – 231, DOI: 10.4995/agt.2015.3830.

V. Popa and A.-M. Patriciu, Well posedness of fixed point problem for mappings satisfying an implicit relation in Gp-metric spaces, Mathematical Sciences and Applications E-Notes 3(1) (2015), 108 – 117, DOI: 10.36753/mathenot.421226.

V. Popa and M. Mocanu, Altering distance and common fixed points under implicit relations, Hacettepe Journal of Mathematics and Statistics 38(3) (2009), 329 – 337, URL: https://www.researchgate.net/publication/229012335.

S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publications de l’Institut Mathématique 32 (1982), 149 – 153, http://elib.mi.sanu.ac.rs/files/journals/publ/52/24.pdf.

A. Tomar, R. Sharma, S. Upadhyay and S. Beloul, Common fixed point theorems in Gp metrics spaces and applications, Bulletin of the International Mathematical Virtual Institute 8 (2018), 561 – 574, DOI: 10.7251/BIMVI1803561T.

DOI: http://dx.doi.org/10.26713%2Fcma.v11i3.1402

### Refbacks

- There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905