Discussion on relation-theoretic for JS-quasi-contractions of uni/milti-dimensional mappings with transitivity
Keywords:Transitive relation, Fixed point of N-order
We introduce the notion of a JSR quasi-contraction mapping, where R is a binary relation on its domain. Also, we prove some fixed point results for such contractions in complete metric spaces endowed with a transitive relation. An example is given to substantiate our obtained theorems. In addition, we introduce a JSRN -quasicontraction and also establish fixed point of N-order theorems for such contractions.
S. Banach, “Sur les óperations dans les ensembles abstraits et leurs applications aux équations intégrales”, Fundamenta mathematicae, vol. 3, no. 1, pp. 133-181, 1922. [On line]. Available: https://bit.ly/2XmuBvp
A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations”, Proceedings of the American Mathematical Society, vol. 132, no. 05, pp. 1435–1444, May 2004, doi: 10.1090/S0002-9939-03-07220-4
A. Alam and M. Imdad, “Relation-theoretic contraction principle”, Journal of fixed point theory and applications, vol. 17, no. 4, pp. 693–702, Jul. 2015, doi: 10.1007/s11784-015-0247-y
D. Guo and V. Lakshmikantham, “Coupled fixed points of nonlinear operators with applications”, Nonlinear analysis: theory, methods & applications, vol. 11, no. 5, pp. 623–632, 1987, doi: 10.1016/0362-546X(87)90077-0
T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear analysis: theory, methods & applications, vol. 65, no. 7, pp. 1379–1393, Oct. 2006, doi: 10.1016/j.na.2005.10.017
M. S. Asgari and B. Mousavi, “Coupled fixed point theorems with respect to binary relations in metric spaces”, Journal of nonlinear sciences and applications, vol. 08, no. 02, pp. 153–162, Mar. 2015, doi: 10.22436/jnsa.008.02.07
B. Samet and C. Vetro, “Coupled fixed point, F-invariant set and fixed point of N-order”, Annals of functional analysis, vol. 1, no. 2, pp. 46–56, 2010, doi: 10.15352/afa/1399900586
D. Wardowski, “Fixed points of a new type of contractive mappings in complete metric spaces”, Fixed point theory and applications, vol. 2012, Art ID. 94, Jun. 2012, doi: 10.1186/1687-1812-2012-94
F. Khojasteh, S. Shukla, and S. Radenovic, “A new approach to the study of fixed point theory for simulation functions”, Filomat, vol. 29, no. 6, pp. 1189–1194, 2015., doi: 10.2298/FIL1506189K
L. Ćirić, “Generalized contractions and fixed-point theorems”, Publications de l'Institut Mathématique (Online), vol. 12, no. 26, pp.19-26, 1971, [On line]. Available: https://bit.ly/36njWEQ
L. Ćirić, “A generalization of Banach’s contraction principle”, Proceedings of the American Mathematical Society, vol. 45, no. 2, pp. 267-273, Aug. 1974, doi: 10.2307/2040075
M. Jleli and B. Samet, “A new generalization of the Banach contraction principle”, Journal of inequalities and applications, vol. 2014, no. 1, Art ID. 38, May 2014, doi: 10.1186/1029-242X-2014-38
N. Hussain, V. Parvaneh, B. Samet, and C. Vetro, “Some fixed point theorems for generalized contractive mappings in complete metric spaces,” Fixed point theory and applications, vol. 2015, no. 1, Art ID. 185, Oct. 2015, doi: 10.1186/s13663-015-0433-z.
Z. Li and S. Jiang, “Fixed point theorems of JS-quasi-contractions”, Fixed point theory and applications, vol. 2016, no. 1, Art ID. 40, Mar. 2016, doi: 10.1186/s13663-016-0526-3
S. Lipschutz, Theory and problems of set theory and related topics. New York, NY: McGraw-Hill, 1964.
B. C. Kolman, R. C. Busby, and S. C. Ross, Discrete mathematical structures, 3rd ed. New Delhi: Prentice Hall of India Pvt. Ltd, 2000.
A. F. Roldán López de Hierro, “A unified version of Ran and Reuring’s theorem and Nieto and Rodríguez-Lopez’s theorem and low-dimensional generalizations”, Applied mathematics & information sciences, vol. 10, no. 2, pp. 383–393, Mar. 2016, doi: 10.18576/amis/100201
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