Some common fixed-point theorems for a pair of p-hybrid mappings via common limit range property in G-metric space

Year 2021, Volume: 4 Issue: 2, 87 - 104, 30.06.2021

Lucas Wangwe , Santosh Kumar

https://doi.org/10.53006/rna.907704

Cited By: 2

Abstract

This paper aims to prove common fixed point theorems for a pair of hybrid and p-hybrid mappings via common limit range property in G-metric space setting. The
theorems proved here will generalise the results due to Nashine et al. [35], Karapinar et al. [23, 24] from metric space notion to G-metric space and that of Mustafa et
al.[30] using (CLRf ) property concept in G-metric space, and many others in this setting. We also provided an illustrative example to validate the results.

Keywords

Common fixed point, p-hybrid mapping, common limit range property, G- metric space.

Supporting Institution

None

Project Number

None

Thanks

Thanks

References

• [1] Aamri, M., El Moutawakil, D., Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270(1), (2002), 181–188.
• [2] Agarwal, R. P., Kadelburg, Z., Radenovic, S., On coupled fixed point results in asymmetric G-metric spaces, Journal of operators, 2013(1), (2013).
• [3] Agarwal, R. P., Karapınar, E., O’Regan, D. and Roldan-Lopez-de-Hierro, A. F., Fixed point theory in metric type spaces Fixed Point Theory and Applications, Switzerland: Springer,(2015).
• [4] Ahmad, B., Ashraf, M., Rhoades, B. E., Fixed point theorems for expansive mappings in D-metric spaces, Indian Journal of Pure and Applied Mathematics, 32(10), (2001), 1513–1518.
• [5] Azam. A., Mehmood, N., Fixed point theorems for multivalued mappings in G-cone metric spaces, Journal of Inequalities and Applications, (1), (2013), 354.
• [6] Chauhan, S., Khan, M. A., Kadelburg, Z., Imdad, M., Unified common fixed point theorems for a hybrid pair of mappings via an implicit relation involving altering distance function, Abstract, and Applied Analysis, Volume 2014, (2014), Article ID 718040 | https://doi.org/10.1155/2014/718040.
• [7] Chugh, R., Kadian, T., Rani, A., Rhoades, B. E., Property P in G-metric spaces, Fixed Point Theory, and Applications, (2010), 2010, 12pages.
• [8] Dhage, B. C., Generalised metric space and topological structure, I. Analele Atintifice ale Universitatii Al. I. Cuza din lasi. Serie Noua Mathematica, 46(3), (2000), 24.
• [9] Dhage, B. C., A common fixed point principle in D-metric spaces, Bulletin of the Calcutta Mathematical Society, 91(6), (1999), 475–480.
• [10] Dhage, B. C., Pathan, A. M., Rhoades, B. E., A general existence principle for fixed point theorems in D-metric spaces, International Journal of Mathematics and Mathematical Sciences, 23(7), (2000), 441–448.
• [11] Fisher, B., Mappings with a common fixed point, Math. Sem. Notes Kobe Univ., 7(1979), 115–148.
• [12] Gahler, S., 2-metrische Raume und ihre topologische Struktur, Math. Nachr., (26)(1963), 115–148.
• [13] Gupta, V., Shatanawi, W., Kanwar, A., Coupled Fixed Point Theorems Employing CLR-Property on V-Fuzzy Metric Spaces, Mathematics, 8(3), (2020), p.404.
• [14] Goebel, K. C coincidence theorem, Bull. Acad. Polon. Sci. S6r. Sci. Math., 16 (1968) 733 -735.
• [15] Ha, K. S., Cho, Y. J., White, A., Strictly convex and 2-convex 2-normed spaces, Math. Japonica, 33(3), (1988), 375–384.
• [16] Imdad, M., Chauhan, S. and Kumam, P., Fixed point theorems for two hybrid pairs of non-self mappings under joint common limit range property in metric spaces. J. Nonlinear Convex Anal., 16 (2),( 2015), 243-254.
• [17] Imdad, M., Chauhan, S., Soliman, A. H. and Ahmed, M. A., Hybrid fixed point theorems in symmetric spaces via common limit range property, Math. 47(4), (2014), 949–962.
• [18] Imdad, M., Chauhan, S., Kadelburg, Z., Fixed point theorems for mappings with common limit range property satisfying generalised ( phi,psi)-weak contractive conditions, Mathematical Sciences, 7(1), (2013), p.16.
• [19] Iseki, K., Fixed point theorems in 2-metric spaces, Math. Semin. Notes, Kobe Univ., (3)(1975), 133–136.
• [20] Jleli, M. and Samet, B., Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory and Applications, 2012(1), (2012), p.210.
• [21] Jungck, G., Commuting mappings and fixed points, American Mathematical Monthly, (3)(1978), 261–263.
• [22] Kaewcharoen, A., Kaewkhao, A., Common fixed points for single-valued and multivalued mappings in G-metric spaces, Int. J. Math. Anal, 5 (2011), 1775–1790.
• [23] Karapınar, E., Aydi, H., Fulga, A., On-Hybrid Wardowski Contractions, Journal of Mathematics, (2020), Article ID 1632526, 8 pages https://doi.org/10.1155/2020/1632526
• [24] Karapınar, E., Alqahtani, O. and Aydi, H., On interpolative Hardy-Rogers type contractions, Symmetry, 11(1), ( 2019), 8.
• [25] Khan, M. S., On the convergence of sequences of fixed points in 2-metric spaces, Indian Journal of Pure and Applied Mathematics, 10(9), (1979), 1062–1067.
• [26] Kubiak, T., Common fixed points of pairwise commuting mappings, Math. Nachr., (118), (1984), 123–127.
• [27] Mustafa, Z., Aydi, H., Karapınar, E., On common fixed points in G-metric spaces using (EA) property, Comput. Math. Appl., 64(6),(2012), 1944–1956.
• [28] Mustafa, Z., Obiedat, H., A fixed points theorem of Reich in G-metric spaces, Cubo A Mathematics Journal, 12(1), (2010), 83–93.
• [29] Mustafa, Z., Sims, B., Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory and Applications, (2009), 1–10.
• [30] Mustafa, Z., Shatanawi, W., Bataineh, M., Existence of fixed point results in Gmetric spaces, International Journal of Mathematics and Mathematical Sciences, (2009), 1–10.
• [31] Mustafa, Z., Arshad, M., Khan, S.U., Ahmad, J. and Jaradat, MMM, Common fixed points for multivalued mappings in G-metric spaces, J. Nonlinear Sci. Appl., 10 (2017), 2550–2564.
• [32] Mustafa, Z., Sims, B., A new approach to generalised metric spaces, Journal of Non-linear and convex Analysis, 7(2), (2006), 289–297.
• [33] Nagaraju, V., Common Fixed Point Theorems for Six Self-Maps in G-metric spaces, Annals of Pure and Applied Mathematics, 22(1), (2020), 57–64.
• [34] Naimpally, S. A., Singh, S. L. J. and Whitfield, H. M., Coincidence theorems for hybrid contractions, Math. Nachr. 127 (1986), 177–180.
• [35] Nashine, H. K., Imdad, M., Ahmadullah, M., Common Fixed-Point Theorems for Hybrid Generalized (F; psi)-Contractions Under the Common Limit Range Property with Applications, Ukrainian Mathematical Journal, 69(11),(2018), 1784–1804.
• [36] Popa, V., Patriciu, A.M., A general fixed point theorem for a pair of self mappings with common limit range property in G-metric spaces, Facta Universitatis, Series: Mathematics and Informatics, 29(4),(2015), 351-370.
• [37] Popa, V., Patriciu, A.M., Fixed point theorems for two pairs of mappings satisfying common limit range property in G-metric spaces, Bul. Inst. Politeh. Iasi, Sect. I, Mat. Mec. Teor. Fiz, 62(66), (2016), 19–42.
• [38] Popa, V., Fixed point theorems for two pairs of mappings satisfying a new type of common limit range property, Filomat, 31(11), (2017), 3181–3192.
• [39] Rani, A., Kumar, S., Kumar, N., Garg, S. K., Common fixed point theorems for compatible and weakly compatible maps in G-metric spaces, Facta Universitatis, Series: Mathematics and Informatics, 2012(3), (2012), 1128-1134.
• [40] Rhoades, B. E., A fixed point theorem for generalised metric spaces, Internat. J. Math. & Math. Sci., 19(3),(1996), 457–460.
• [41] Rhoades, B. E., Contraction type mappings on a 2-metric space,Math. Nachr. 91 (1979), 151–155.
• [42] Sedghi, S., Nabi, S., Haiyun, Z., A common fixed point theorem in metric spaces, Fixed point theory and Applications, 2007, (2007), 13.
• [43] Shatanawi, W. A, Abbas M. Some fixed point results for multivalued mappings in ordered G-metric spaces, Gazi University Journal of Science, 25(2), (2012), 385–92.
• [44] Shoaib, A., Shahzad, A., Common Fixed Point of Multivalued Mappings in Ordered Dislocated Quasi G-Metric Spaces, Punjab University Journal of Mathematics, 52(10), (2020).
• [45] Singh, B., Sharma, R. K., Common fixed points via compatible maps in D-metric spaces, International Journal of Mathematics and Mathematical Sciences, 11(1), (2002), 145–153.
• [46] Sintunavarat, W. and a Kumam, P., Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., (2011), 1–14.
• [47] Sushanta, K. M., Property P of Ciric operators in G-metric spaces, Inter. J. of Math. Sci. and Engg. Appls., 5(2), (2011), 353–367.
• [48] Tahat, N., Aydi, H., Karapınar, E., Shatanawi, W., Common fixed points for single-valued and multivalued maps satisfying a generalised contraction in G-metric spaces, Fixed Point Theory Appl., 10, (2012), 1–9.
• [49] Khan, M. On fixed point theorems in 2-metric space, Publ. de l’Institute Math’ematique, 41 (1980), 107–112.