Browse > Article
http://dx.doi.org/10.22771/nfaa.2021.26.01.13

COINCIDENCE AND FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTION MAPPING ON b-METRIC SPACES  

Malkawi, Abed Al-Rahman M. (Department of Mathematics, Faculty of Science The University of Jordan)
Talafhah, Abdallah (Department of Mathematics, Faculty of Science The University of Jordan)
Shatanawi, Wasfi (Department of General Sciences Prince Sultan University)
Publication Information
Nonlinear Functional Analysis and Applications / v.26, no.1, 2021 , pp. 177-195 More about this Journal
Abstract
In this paper, we introduce the modification of a generalized (Ψ, L)-weak contraction and we prove some coincidence point results for self-mappings G, T and S, and some fixed point results for some maps by using a (c)-comparison function and a comparison function in the sense of a b-metric space.
Keywords
b-metric space; (${\Psi}$, L)-weak contraction; comparison function; (c)-comparison function;
Citations & Related Records
연도 인용수 순위
  • Reference
1 M. Abbas, W. Shatanawi, S. Farooq and Z.D. Mitrovic, On a JH-operators pair of type (A) with applications to integral equations, J. Fixed Point Theory Appl., 22 (2020), Article number 72.
2 K. Abodayeh, T. Qawasmeh, W. Shatanawi and A. Tallafha, Eϕ-contraction and some fixed point results via modified -distance mappings in the frame of complete quasi metric spaces and applications, Inter. J. Elect. Comput. Eng., 10 (2020), 3839-3853.   DOI
3 A. Aghajani, M. Abbas and J.R. Roshan, common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960.   DOI
4 E. Ameer, H. Aydi, H.A. Hammad, W. Shatanawi and N. Mlaiki, On (ϕ, ψ)-metric spaces with applications, Symmetry, 12 (2020), Article number 1459.
5 H. Aydi, W. Shatanawi, M, Postolache, Z. Mustafa and N. Tahat, Theorems for Boyd-Wong-type contractions in ordered metric spaces, Abst. Appl. Anal., 2012 (2012), Article number 359054.
6 I.A. Bakhtin, The contraction mapping principle in almost metric spaces., Funct. Anal., 30 (1989), 26-37.
7 M. Boriceanu, Fixed point theory for multivalued generalized contractions on a set with two b-metric, Creative Math Inf., 17 (2008), 326-332.
8 A. Bataihah, W. Shatanawi, T. Qawasmeh and R. Hatamleh, On H-Simulation functions and fixed point results in the setting of wt-distance mappings with application on matrix equations, Mathematics, 8(5) (2020), Article number 837.
9 A. Bataihah, W. Shatanawi and A. Tallafha, Fixed point results with simulation functions, Nonlinear Funct. Anal. Appl., 25(1) (2020), 13-23.
10 A. Bataihah, A. Tallafha and W. Shatanawi, Fixed point results with Ω-distance by utilizing simulation functions, Italian J. Pure and Appl. Math., 43 (2020), 185-196.
11 S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostra. 1 (1993), 5-11.
12 H. Huang and SH. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl., 2013:112. (2013).
13 U. Kadak, On the classical sets of sequences with fuzzy b-metric, Gen. Math. Notes. 23(1) (2014), 89-108.
14 T. Kamran, M. Samreen and Q. Ain. A Generalization of b-Metric space and some fixed point theorems, Acta Math. Inform. Univ. Ostra. 5(19) (2017).
15 M. Pacurar, A fixed point results for ϕ-contraction on b-metric spaces without the boundedness assumption, Fasciculi Math., 43 (2010), 127-136.
16 A. Khan, T. Abdeljawad, W. Shatanawi and H. Khan, Fixed point theorems for quadruple self-mappings satisfying integral type inequalities, Filomat, 34(3) (2020), 905-917 https://doi.org/10.2298/FIL2003905K   DOI
17 A. Mukheimer, N. Mlaiki, K. Abodayeh and W.Shatanawi, New theorems on extended b-metric spaces under new contractions, Nonlinear Anal, Model. Control, 24(6) (2019), 870-883.
18 K. Kukic, W. Shatanawi and M.G. Filipovic, Khan and Ciric contraction princples in almost b-metric space, U.P.B. Sci. Bull., Series A, 82(1) (2020).
19 Z. Mustafa, J.R. Roshan and V. Parvaneh, Coupled coincidence point results for (ψ, ϕ)-weakly counteractive mappings in partially ordered Gb-metric spaces, Fixed Point Theory Appl., (2013), 2013:206.
20 M. Pacurar, Sequences of almost contractions and fixed points in b-metric spaces, Analele Universitatii de Vest, Timisoara Seria Mate. Inform., XLVIII., 3 (2010), 125-137.
21 V. Parvaneh, J.R. Roshan and S. Radenovic, Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations, Fixed point Theory Appl., (2013), 2013:130.
22 H. Qawaqneh, M. S. M. Noorani and W. Shatanawi, Fixed point theorems for (α, k, θ)-contractive multi-valued mapping in b-metric space and applications, Int. J. Math. Comput. Sci., 14(1) (2019), 263-283.
23 H. Qawaqneh, M.S.M. Noorani, S. Shatanawi, H. Aydi and H. Alsamir, Fixed point results for multi-valued contractions in b-metric spaces and an application, Mathematics, 7 (2019), Article number 132.
24 J.R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei and W. Shatanawi, Common fixed points of almost generalized (ψ, ϕ)s-contractive mappings in ordered bmetric spaces, Fixed Point Theory Appl., (2013), 2013:159, 123.   DOI
25 T. Qawasmeh, A. Tallafha and W. Shatanawi, Fixed and common fixed point theorems through modified ω-distance mappings, Nonlinear Funct. Anal. Appl., 24 (2019), 221-239.
26 T. Qawasmeh, A. Tallafha and W. Shatanawi, Fixed point theorems through modified ω-distance and application to nontrivial equations, Axioms, 8 (2019), Article Number 57.
27 K.P.R. Rao, W. Shatanawi, G.N.V. Kishore, K. Abodayeh and D.R. Prasad, Existeness and uniqeness of Suzuki type results in Sbmetric spaces with applications to Integral equations, Nonlinear Funct. Anal. Appl., 23 (2018), 225-245.   DOI
28 S. Sedghi, N. Shobkolaei, J. Rezaei Roshan, and W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Matematicki Vesnik, 66(2) (2014), 190-201.
29 W. Shatanawi, Fixed and common fixed point for mappings satisfying some nonlinear contractions in b-metric spaces, J. Math. Anal., 7(4) (2016), 1-12.
30 W. Shatanawi, On w-compatible mappings and common coupled coincidence point in cone metric spaces, Appl. Math. Letters, 25 (2012), 925-931.   DOI
31 W. Shatanawi, Some fixed point results for a generalized weak contraction mappings in orbitally metric spaces, Chaos, Solitons and Fractals, 45 (2012), 520-526.   DOI
32 W. Shatanawi, K. Abodayeh and A. Mukheimer, Some fixed point theorems in extended bmetric spaces, U.P.B. Sci. Bull., 80 (218), 71-78.
33 W. Shatanawi and M. Postolache, Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), Article number 271.
34 W. Shatanawi, A. Bataihah and A. Tallafha, Four-step iteration scheme to approximate fixed point for weak contractions, Comput. Materials Continua CMC, 64 (2020), 1491-1504.   DOI
35 W. Shatanawi, E. Karapnar and H. Aydi, Coupled coincidence points in partially ordered cone metric spaces with a c-distance, J. Appl. Math., 2012 (2012), Article number 312078.
36 W. Shatanawi, Z. Mustafa and N. Tahat, Some coincidence point theorems for nonlinear contraction in ordered metric spaces, Fixed Point Theory Appl., 2011 (2011), Article number 68.
37 W. Shatanawi and A. Pitea, Fixed and coupled fixed point theorems of omega-distance for nonlinear contraction, Fixed Point Theory App., 2013(11) (2013), DOI: 10.1186/1687-1812-2013-275.   DOI
38 W. Shatanawi, A. Pitea and R. Lazovi, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl., 2013(120) (2013).
39 W. Shatanawi and M. Postolache, Common fixed point theorems for dominating and weak annihilator mappings in ordered metric spaces, Fixed Point Theory Appl., 2013 (2013), Article number 271.
40 W. Shatanawi, V.C. Rajic, S.C. Radenovic and A. Al-Rawashdeh, Mizoguchi-Takahashi-type theorems in tvs-cone metric spaces, Fixed Point Theory and Appl., 2012 (2012), Article number 106.