On relation-theoretic F−contractions and applications in F−metric spaces

Anita Tomar; Meena Joshi; S. K. Padaliya

doi:10.2478/ausm-2023-0018

Abstract

The aim is to introduce some relation theoretic variants of F−contraction in an F−metric space endowed with a binary relation R and to prove results for its fixed point. In the sequel, several classes of contractions are sharpened, generalized, and improved. Numerical examples are presented to illustrate the theoretical conclusions. As applications of the main results, we solve a Dirichlet-Neumann initial value problem and two Dirichlet boundary value problems.

References

A. Alam, M. Imdad, Relation-theoretic contraction principle, J. Fixed Point Theory Appl., 17(4), (2015), 693–702.
Search in Google Scholar Back to article
A. Alam, M. Imdad, Relation-theoretic metrical coincidence theorems, Filomat, (2017), 4421–4439.
Search in Google Scholar Back to article
L. A. Alnaser, D. Lateef, H. A. Fouad, J. Ahmad, Relation theoretic contraction results in F−metric spaces, J. Nonlinear Sci. Appl., 12, (2019), 337–344.
Search in Google Scholar Back to article
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équation intégrales, Fund. Math., 3, (1922), 133–181.
Search in Google Scholar Back to article
Lj. B.Ćirić, A generalization of Banach’s contraction principle, Proc. Am. Math. Soc., 45, (1974), 267–273.
Search in Google Scholar Back to article
S. K. Chatterjea, Fixed-point theorems, Comptes Rendus de L’Academie Bulgare des Sciences, 25(6), (1972), 727–730.
Search in Google Scholar Back to article
M. Cosentino, P. Vetro, Fixed point results for F−contractive mappings of Hardy-Rogers-type, Filomat, 28(4), (2014), 715–722.
Search in Google Scholar Back to article
G. E. Hardy, T. D. Rogers, A generalization of a fixed point theorem of Reich, Cand. Math. Bull., 16(2), (1973), 201–206.
Search in Google Scholar Back to article
M. Jleli, B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl., 20(3), (2018), 1–20.
Search in Google Scholar Back to article
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc., 60, (1968), 71–76.
Search in Google Scholar Back to article
W. Kirk, N. Shahzad, Fixed point theory in distance spaces, Springer, Cham, 2014.
Search in Google Scholar Back to article
B. Kolman, R. C. Busby, S. Ross, Discrete Mathematical Structures, Third Edition, PHI Pvt. Ltd., New Delhi, (2000).
Search in Google Scholar Back to article
M. A. Kutbi, A. Roldán, W. Sintunavarat, J. Martinez-Moreno, C. Roldán, F−closed sets and coupled fixed point theorems without the mixed monotone property, Fixed Point Theory Appl., 2013(1), (2013), 1–11.
Search in Google Scholar Back to article
S. Lipschutz, Schaum’s outlines of theory and problems of set theory and related topics, McGraw-Hill, New York, (1964).
Search in Google Scholar Back to article
R. D. Maddux, Relation algebras, studies in Logic and the Foundations of Mathematics, Elsevier B. V., Amsterdam, 150, (2006).
Search in Google Scholar Back to article
J. J. Nieto, R. Rodŕiguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22(3), (2005), 223–239.
Search in Google Scholar Back to article
A. Petru¸sel, G. Petru¸sel, Yi-Bin Xiao, J.-C. Yao, Fixed point theorems for generalized contractions with applications to coupled fixed point theory, J. Nonlinear Convex Anal., 19(1), (2018), 71–88.
Search in Google Scholar Back to article
A. C. M. Ran, M. C. Reurings, A fixed point theorem in partially ordered set and some applications to matrix equation, Proc. Amer. Math. Soc., 132, (2004), 1435–1443.
Search in Google Scholar Back to article
S. Reich, Some remarks concerning contraction mappings, Can. Math. Bull., 14(1), (1971), 121–124.
Search in Google Scholar Back to article
A. F. Roldán, Lòpez de Hierro A unified version of Ran and Reurings theorem and Nieto and Rodríguez-Lópezs theorem and low-dimensional generalizations, Appl. Math. Inf. Sci., 10(2), (2016), 383–393.
Search in Google Scholar Back to article
B. Samet, M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications, Commun. Math. Anal., 13(2), (2012), 82–97.
Search in Google Scholar Back to article
M. Turinici, Ran-Reurings fixed point results in ordered metric spces, Libertas Math., 31, (2011), 49–55.
Search in Google Scholar Back to article
A. Tomar, C. Giniswamy, Jeyanthi, and P. G. Maheshwari, On coincidence and common fixed point of six maps satisfying F-contractions, TWMS J. App. Eng. Math., 6(2), (2016), 224–231.
Search in Google Scholar Back to article
A. Tomar, C. Giniswamy, Jeyanthi, and P. G. Maheshwari, Coincidence and common fixed point of F-contractions via CLRST property, Surv. Math. Appl., 11, (2016), 21–31.
Search in Google Scholar Back to article
A. Tomar and R. Sharma, Almost alpha-Hardy-Rogers-F-contractions and applications, Armen. J. Math., 11(11), (2019), 1–19.
Search in Google Scholar Back to article
A. Tomar, M. Joshi, S. K. Padaliya, B. Joshi, A. Diwedi, Fixed point under set-valued relation-theoretic nonlinear contractions and application. Filomat 33(14), (2019), 4655–4664.
Search in Google Scholar Back to article
A. Tomar and M. C. Joshi, “Fixed Point Theory & its Applications to Real World Problem”, Nova Science Publishers, New York, USA, 2021. ISBN978-1-53619-336-7
Search in Google Scholar Back to article
A. Tomar, M. Joshi, Relation-theoretic nonlinear contractions in an F−metric space and applications, Rend. Circ. Mat. Palermo, 70(2), (2021), 835–852.
Search in Google Scholar Back to article
D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. 94, (2012).
Search in Google Scholar Back to article

On relation-theoretic F−contractions and applications in F−metric spaces

Abstract

Paradigm

My account