Best proximity points for generalized (F, R)-proximal contractions
Abstract
We present the notion of generalized (F, R)-proximal non-self contractions and prove best proximity point theorems in complete metric spaces endowed with an arbitrary binary relation. An example is given to vindicate our claims. We also show that the edge preserving structure is a particular case of the binary relation R. Moreover, an application to variational inequality problem is given in order to demonstrate the efficacy of our results.
Downloads
References
Alam, A., Imdad, M., Relation-theoretic contraction principle, J. Fixed Point Theory Appl. 17(4), 693-702, (2015).
Alam, A., Imdad, M. Relation-theoretic metrical coincidence theorems, Filomat 31, 4421–4439, (2017).
Alam, A., Imdad, M., Monotone generalized contractions in ordered metric spaces, Bull. Korean Math. Soc. 53(1), 61-81, (2016).
Alam, A., Khan, A.R., Imdad, M., Some coincidence theorems for generalized nonlinear contractions in ordered metric spaces with applications, Fixed Point Theory Appl. 216, (2014).
Alam, A., George, R., Imdad, M., Refinements to Relation-Theoretic Contraction Principle, Axioms 11, 316, (2022).
Altun, I., Aslantas, M., Sahin, H., KW-type nonlinear contractions and their best proximity points, Numer. Funct. Anal. Optim. 24, 1-20, (2021).
Altun, I., Aslantas, M., Sahin, H., Best proximity point results for p-proximal contractions, Acta. Math. Hung. 162, 393-402, (2020).
Aslantas, M., Sahin, H., Altun, I., Best proximity point theorems for cyclic p-contractions with some consequences and applications, Nonlinear Anal. Model Control 26(1), 113-129, (2021).
Basha, S.S., Veeramani, P., Best proximity pair theorems for multifunctions with open fibres, J. Approx. Theory 103, 119–129, (2000).
Basha, S.S., Extensions of Banach’s contraction principle, Numer. Funct. Anal. Optim. 31, 569-576, (2010).
Basha, S.S., Best proximity points: optimal solutions, J. Optim. Theory Appl. 151, 210-216, (2011).
Beg, I., Bartwal, A., Rawat, S., Dimri, R.C., Best proximity points in noncommutative Banach spaces, Comp. Appl. Math. 41, 41 (2022).
Debnath, P., Konwar, N., Radenovic, S., Metric fixed point theory: Applications in science, engineering and behavioural sciences, 314-316, (2021).
Dhivya, P., Radenovic, S., Marudai, M., Bin-Mohsin, B., Coupled fixed point and best proximity point results involving simulation functions, Bol. Soc. Paran. Mat. 22, 1–15, (2004).
Eldered, A.A., Veeramani, P., Existence and convergence for best proximity points, J. Math. Anal. Appl. 33, 1001-1006, (2004).
Golubovic, Z., Kadelburg, Z., Radenovic, S., Coupled coincidence points of mappings in ordered partial metric spaces, Abstr. Appl. Anal. Article ID 192581, (2012).
Harjani, J., Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. 71, 3403-3410, (2009).
Jachymski, J., The contraction principle for mappings on a metric space with a graph, Proc. Am. Math. Soc. 136(4), 1359-1373, (2008).
Karapınar, E., Roldan, A., Shahzad, N., Sintunavarat, W., Discussion of coupled and tripled coincidence point theorems for ϕ-contractive mappings without the mixed g-monotone property, Fixed Point Theory Appl. 2014(1), 1-16, (2014).
Lipschitz, S., Schaum’s Outlines of Theory and Problems of Set Theory and Related Topics, McGraw-Hill, New York, (1964).
Raj, V.S. A best proximity point theorem for weakly contractive non-self mappings, Nonlinear Anal. 74(11), 4804–4808, (2011).
Raj, V.S., Best proximity point theorems for nonself mappings, Fixed Point Theory 14(2), 447-454, (2013).
Rawat, S., Dimri, R.C., Bartwal, A., F-Bipolar metric spaces and fixed point theorems with applications, J. Math. Comput. SCI-JM. 26(2), 184-195, (2022).
Rawat, S., Kukreti, S., Dimri, R.C., Fixed point results for enriched ordered contractions in noncommutative Banach spaces, J. Anal. 30, 1555-1566, (2022).
Sahin, H., Aslantas, M., Altun, I., Feng-Liu type approach to best proximity point results for multivalued mappings, J. Fixed Point Theory Appl. 22(1), 1-13, (2020).
Sultana, A., Vetrivel, V., On the existence of best proximity points for generalized contractions, Appl. Gen. Topol. 15(1), 55-63, (2014).
Samet, B., Turinici, M., Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Commun. Math. Anal. 13(2), 82-97, (2012).
Senapati, T., Dey, L.K., Relation-theoretic metrical fixed point results via w-distance with applications, J. Fixed Point Theory Appl. 19, 2945-2961, (2017).
Turinici, M., Abstract comparison principles and multi-variable Gronwall-Bellman inequalities, J. Math. Anal. Appl. 117(1), 100-127, (1986).
Turinici, M., Contractive operators in relational metric spaces, Handbook of Functional Equations, Optimization and Its Appl., Springer, 95, 419-458, (2014).
Turinici, M., Fixed points for monotone iteratively local contractions, Dem. Math. 19(1), 171-180, (1986).
Turinici, M., Nieto-Lopez theorems in ordered metric spaces, Math. Student 81(4), 219-229, (2012).
Turinici, M., Ran-Reuring’s theorems in ordered metric spaces, J. Indian Math. Soc. 78, 207-214, (2011).
Wardowski, D., Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 2012, 94, (2012).
Copyright (c) 2024 Boletim da Sociedade Paranaense de Matemática
This work is licensed under a Creative Commons Attribution 4.0 International License.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Funding data
-
Council of Scientific and Industrial Research, India
Grant numbers 09/386(0064)/2019-EMR-I
