In this paper, we prove some coincidence point theorems for weak C-contractions and K-contractions involving a new auxiliary function in a metric space endowed with a locally $ f $-transitive binary relation. In this context, we generalize some relevant fixed point results in the literature. Further, we give an example to substantiate the utility of our results.
Citation: Faruk Sk, Asik Hossain, Qamrul Haq Khan. Relation-theoretic metrical coincidence theorems under weak C-contractions and K-contractions[J]. AIMS Mathematics, 2021, 6(12): 13072-13091. doi: 10.3934/math.2021756
In this paper, we prove some coincidence point theorems for weak C-contractions and K-contractions involving a new auxiliary function in a metric space endowed with a locally $ f $-transitive binary relation. In this context, we generalize some relevant fixed point results in the literature. Further, we give an example to substantiate the utility of our results.
| [1] |
S. Banach, Sur les operations dans les ensembles abstraints er leur application aux equations intgrales, Fund. Math., 3 (1922), 133–181. doi: 10.4064/fm-3-1-133-181
|
| [2] |
A. Ali, H. Işık, H. Aydi, E. Ameer, J. R. Lee, M. Arshad, On multivalued SU-type θ-contractions and related applications, Open Math., 18 (2020), 386–399. doi: 10.1515/math-2020-0139
|
| [3] |
A. Ali, F. Uddin, M. Arshad, M. Rashid, Hybrid fixed point results via generalized dynamic process for F-HRS type contractions with application, Phys. A. Stat. Mech. Appl., 538 (2020), 122669. doi: 10.1016/j.physa.2019.122669
|
| [4] | A. Ali, M. Alansari, F. Uddin, M. Arshad, A. Asif, G. A. Basendwah, Set-valued SU-type fixed point theorems via Gauge function with applications, J. Math., (2021), 6612448. |
| [5] | R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60 (1968), 71–76. |
| [6] | S. K. Chatterjea, Fixed-point theorems, Comptes Rendus de l'Académie Bulgare des Sci., 25 (1972), 727–730. |
| [7] | B. S. Choudhury, Unique fixed point theorem for weak C-contractive mappings, Kathmandu Univ. J. Sci., Eng. Technol., 5 (2009), 6–13. |
| [8] |
A. Razani, V. Parvaneh, Some fixed point theorems for weakly T-Chatterjea and weakly T-Kannan-contractive mappings in complete metric spaces, Russ. Math. (Izv. VUZ), 57 (2013), 38–45. doi: 10.3103/S1066369X13030055
|
| [9] |
A. Alam, M. Imdad, Relation-theoretic contraction principle, J. Fixed Point Theory Appl., 17 (2015), 693–702. doi: 10.1007/s11784-015-0247-y
|
| [10] | M. U. Ali, Y. Guo, F. Uddin, H. Aydi, K. Javed, Z. Ma, On partial metric spaces and related fixed point results with applications, J. Funct. Spaces, (2020), 6671828. |
| [11] | P. Gopi, K. Deepak, Fixed point theorems in relational metric spaces with an application to boundary value problems, J. Part. Differ. Equ., 34 (2021), 83–93. |
| [12] | F. Uddin, C. Park, K. Javed, M. Arshad, J. R. Lee, Orthogonal m-metric spaces and an application to solve integral equations, Adv. Differ. Equ., (2021), 159. |
| [13] |
A. Alam, M. Imdad, Nonlinear contractions in metric spaces under locally $T$-transitive binary relations, Fixed Point Theory, 19 (2018), 13–24. doi: 10.24193/fpt-ro.2018.1.02
|
| [14] |
H. A. Hammad, M. De la Sen, A solution of Fredholm integral equation by using the cyclic $\eta^{q}_{s}$-rational contractive mappings technique in b-metric-like spaces, Symmetry, 11 (2019), 1184. doi: 10.3390/sym11091184
|
| [15] | H. A. Hammad, M. De la Sen, Solution of nonlinear integral equation via fixed point of cyclic $\alpha ^{\psi}_{L}$-rational contraction mappings in metric-like spaces, Bull. Braz. Math. Soc. New Ser., 51 (2020), 81–105. |
| [16] | H. A. Hammad, M. De la Sen, A coupled fixed point technique for solving coupled systems of functional and nonlinear integral equations, Mathematics, 7 (2019), 634. |
| [17] |
G. Jungck, Commuting maps and fixed points, Amer. Math. Mon., 83 (1976), 261–263. doi: 10.1080/00029890.1976.11994093
|
| [18] | G. Jungck, Common fixed points for noncontinuous non self maps on non-metric space, Far. East. J. Math. Sci., 4 (1996), 199–215. |
| [19] | S. Lipschutz, Schaum's outlines of theory and problems of set theory and related topics, McGraw-Hill, New York, 1964. |
| [20] | R. D. Maddux, Relation algebras, studies in logic and the foundations of mathematics, Elsevier, Amsertdam, 2006. |
| [21] | V. Fla$\check{s}$ka, J. Je$\check{z}$ek, T. Kepka, J. Kortelainen, Transitive closures of binary relations I, Acta Univ. Carolin. Math. Phys., 48 (2007), 55–69. |
| [22] |
H. L. Skala, Trellis theory, Algebr. Univ., 1 (1971), 218–233. doi: 10.1007/BF02944982
|
| [23] |
A. Stouti, A. Maaden, Fixed point and common fixed point theorems in pseudo-ordered sets, Proyecciones, 32 (2013), 409–418. doi: 10.4067/S0716-09172013000400008
|
| [24] | B. Samet, M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Commun. Math. Anal., 13 (2012), 82–97. |
| [25] | B. Kolman, R. C. Busby, S. Ross, Discrete mathematical structures, 3 Eds, PHI Pvt. Ltd., New Delhi, 2000. |
| [26] | A. Alam, M. Imdad, Relation-theoretic metrical coincidence theorems, Filomat, 31 (2015), 693–702. |
| [27] | S. Sessa, On a weak commutativity conditon of mappings in fixed point consideration, Publ. Inst. Math. Soc., 32 (1982), 149–153. |
| [28] |
G. Jungck, Compatible mappings and common fixed points, Int. J. Math. Sci., 9 (1986), 771–779. doi: 10.1155/S0161171286000935
|
| [29] | A. F. Roldán-López-de-Hierro, E. Karapinar, M. de la sen, Coincidence point theorems in quasi-metric spaces without assuming the mixed monotone property and consequences in G-metric spaces, Fixed Point Theory Appl., (2014), 184. |
| [30] |
J. Harjani, B. López, K. Sadarangani, Fixed point theorems for weakly C-contractive mappings in ordered metric spaces, Comput. Math. Appl., 61 (2011), 790–796. doi: 10.1016/j.camwa.2010.12.027
|
Faruk Sk, Asik Hossain, Qamrul Haq Khan. Relation-theoretic metrical coincidence theorems under weak C-contractions and K-contractions[J]. AIMS Mathematics, 2021, 6(12): 13072-13091. doi: 10.3934/math.2021756
DownLoad: