A New Approach to Multivalued Certain Contraction Mappings

Cafer Aydın, Seher Sultan Yeşilkaya


In the submit study, we establish the notion of generalization of partial Hausdorff metric space. Also, we state an extension of the concept of \(f\)-weak compatibility of Pathak [12] on metric space in generalization of partial metric space. We introduced some common fixed point theorems for multivalued mappings satisfying generalized weak contraction conditions on a complete \(G_p\) metric spaces. Also, a example is given to illustrate the main theorem. Further, our theorems generalize several formerly obtained fixed point results.


Fixed point; \(f\)-weakly compatible mappings; \(G_p\)-metric space; Multivalued mappings

Full Text:



Y. I. Alber and S. Guerre-Delabriere, Principle of weakly contractive maps in Hilbert spaces, in New Results in Operator Theory and its Applications, I. Gohberg and Y. Lyubich (editor), Birkhäuser, Basel (1997), pp. 7 – 22, DOI: 10.1007/978-3-0348-8910-0_2.

N. Assad and W. Kirk, Fixed point theorems for set-valued mappings of contractive type, Pacific Journal of Mathematics 43(3) (1972), 553 – 562, https://projecteuclid.org/euclid.pjm/1102959350.

H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler’s fixed point theorem on partial metric spaces, Topology and its Applications 159(14) 159 (2012), 3234 – 3242, DOI: 10.1016/j.topol.2012.06.012.

H. Aydi, E. Karapıınar and P. Salimi, Some fixed point results in Gp metric spaces, Journal of Applied Mathematics 2012 (2012), Article ID 891713, 15 pages, DOI: 10.1155/2012/891713.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae 3 (1922), 133 – 181, DOI: 10.4064/fm-3-1-133-181.

S. B. Choudhurya and A. Kundub, ((phi,alpha,beta))-weak contractions in partially ordered metric spaces, Applied Mathematics Letters 25 (2012), 6 – 10, DOI: 10.1016/j.aml.2011.06.028.

D. Doric, Common fixed point for generalized ((phi,psi))-weak contractions, Applied Mathematics Letters 22(2) (2009), 1896 – 1900, DOI: 10.1016/j.aml.2009.08.001.

P. N. Dutta and B. S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory and Applications 1 (2008), Article ID 406368, DOI: 10.1155/2008/406368.

L. Gajic, Z. Kadelburg and S. Radenovic, Gp-metric spaces-symmetric and asymmetric, Scientific Publications of the State University of Novi Pazar Ser. A. Appl. Math. Inform. and Mech. 9(1) (2017), 37 – 46, http://scindeks-clanci.ceon.rs/data/pdf/2217-5539/2017/2217-55391701037G.pdf.

A. Kaewcharoen and A. Kaewkhao, Common fixed points for single valued and multivalued mapping in G metric spaces, International Journal of Mathematical Analysis 5(36) (2011), 1775 – 1790, http://www.m-hikari.com/ijma/ijma-2011/ijma-33-36-2011/kaewcharoenIJMA33-36-2011.pdf. .

S. B. Nadler, Multivalued contraction mappings, Pacific Journal of Mathematics 30(2) (1969), 475 – 488, https://msp.org/pjm/1969/30-2/pjm-v30-n2-p12-s.pdf.

H. K. Pathak, Fixed points for weak compatible multi-valued and single-valued mapping, Acta Mathematica Hungarica 67(1-2) (1995), 69 – 78, DOI: 10.1007/BF01874520.

B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Analysis 47(4) (2001), 2683 – 2693, DOI: 10.1016/S0362-546X(01)00388-1.

M. R. A. Zand and A. D. Nezhad, A generalization of partial metric spaces, Journal of Contemporary Applied Mathematics 24 (2011), 86 – 93, https://www.researchgate.net/publication/284286285_A_generalization_of_partial_metric_spaces.

DOI: http://dx.doi.org/10.26713%2Fcma.v11i2.1330


  • There are currently no refbacks.

eISSN 0975-8607; pISSN 0976-5905