Filomat 2023 Volume 37, Issue 4, Pages: 1167-1185
https://doi.org/10.2298/FIL2304167N
Full text (
260 KB)
Cited by
The (ψ,φ)-orthogonal interpolative contractions and an application to fractional differential equations
Nazam Muhammad (Department of Mathematics, Allama Iqbal Open University, Islamabad, Pakistan), muhammad.nazam@aiou.edu.pk
Javed Khalil (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan), khaliljaved15@gmail.com
Arshad Muhammad (Department of Mathematics and Statistics, International Islamic University, Islamabad, Pakistan), marshadzia@iiu.edu.pk
In this manuscript, we introduce the (Ψ,Φ)-orthogonal interpolative
contraction as a generalization of an orthogonal interpolative contraction.
We prove several fixed point theorems stating conditions under which
(Ψ,Φ)-orthogonal interpolative contraction admits a fixed point. Our fixed
point results are improvements of several known results in literature. As an
application, we resolve a fractional differential equation.
Keywords: fixed point, (Ψ, Φ)-orthogonal interpolative contractions, complete O-metric space, application
Show references
H. Afshari, H. Shojaat, M. S. Moradi, Existence of the positive solutions for a tripled system of fractional differential equations via integral boundary conditions, Results in Nonlinear Analysis, 4 (2021) No. 3, 186-199 https://doi.org/10.53006/rna.938851.
H. Afshari, E. Karapinar, A discussion on the existence of positive solutions of the boundary value problems via ψ-Hilfer fractional derivative on b metric spaces, Adv. Differ. Equ. 2020(2020):616. https://doi.org/10.1186/s13662-020-03076-z.
R. P. Agarwal, E. Karapinar, Interpolative Rus-Reich-Ciric type contractions via simulation functions, An. St. Univ. Ovidius Constanta, Ser. Mat., 27(3)(2019), 137-152.
J. Ahmad, A. E. Al-Mazrooei, Y. J. Cho, Y. O. Yang, Fixed point results for generalized Θ-contractions, J. Nonlinear Sci. Appl. 10(2017), 2350-2358.
S. Alizadeh, D. Baleanu, S. Rezapour, Analyzing transient response of the parallel RCL circuit by using the Caputo-Fabrizio fractional derivative, Adv. Differ. Equ. (2020) 2020:55.
A. Amini-Harandi, A. Petrusel, A fixed point theorem by altering distance technique in complete metric spaces, Miskolc Math. Notes 14(2013), 11-17.
A. Atangana, Blind in a commutative world: simple illustrations with functions and chaotic attractors, Chaos Solitons Fractals 114(2018), 347-363.
H. Aydi, E. Karapinar, A.F. Roldan Lopez de Hierro, w-Interpolative Ćirić-Reich-Rus-Type Contractions, Mathematics 2019, 7, 57.
H. Aydi, C.M. Chen, E. Karapinar, Interpolative Ćirić-Reich-Rus type contractions via the Branciari distance, Mathematics, 7(1)(2019), 84.
D. Baleanu, A. Jajarmi, H. Mohammadi, S. Rezapour, A new study on the mathematical modelling of human liver with Caputo-Fabrizio fractional derivative, Chaos, Solitons and Fractals 134 (2020), 109705.
D. Baleanu, H. Mohammadi, Sh. Rezapour, Analysis of the model of HIV-1 infection of CD4+ T-cell with a new approach of fractional derivative, Adv. Differ. Equ. (2020) 2020:71.
H. Baghani, M. E. Gordji, M. Ramezani, Orthogonal sets: The axiom of choice and proof of a fixed point theorem, J. Fixed Point Theory Appl. 18 (2016) 465-477.
I. Beg, G. Mani, A. J. Gnanaprakasam, Fixed point of orthogonal F-Suzuki contraction mapping on 0-complete metric spaces with applications, Journal of Function Spaces, Volume 2021, Article ID 6692112, 12 pages https://doi.org/10.1155/2021/6692112.
D.W. Boyd, J.S.W. Wong, On nonlinear contractions Proc. Am. Math. Soc. 20(1967), 458-464.
F. E. Browder, W. V. Petrysyn The solution by iteration of nonlinear functional equation in Banach spaces, Bull. Amer. Math. Soc. 72 (1966), 571-576.
M. Caputo, M. Fabrizio, A new Definition of Fractional Derivative without Singular Kernel, Progr. Fract. Differ. Appl., 1(2015), 73-85.
K. Diethelm, The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type, Springer, Berlin 2010.
G. Durmaz, I. Altun, Fixed point results for α-admissible multivalued F-contractions, Miskolc Mathematical Notes, 17(1) (2016), 187-199.
Y. U. Gaba, E. Karapinar, A new approach to the interpolative contractions Axioms, 8(4)(2019):110.
P. Gautam, Vishnu N. Mishra, R. Ali, S. Verma, Interpolative Chatterjea and cyclic Chatterjea contraction on quasi-partial b-metric space, AIMS Mathematics, 6(2)(2020), 1727-1742.
M. A. Geraghty, On contractive mappings, Proc. Am. Math. Soc. 40(1973), 604-608.
M. E. Gordji, M. Rameani, M. De La Sen, Y. J. Cho, On orthogonal sets and Banach fixed point theorem, Fixed Point Theory 19(2017), 569-578.
A. Farajzadeh, A. Kaewcharoen, S. Plubtieng, PPF Dependent fixed point theorems for multi-valued mappings in Banach spaces, Bull. Iranian Math. Soc. 42(6) (2016), 1583-1595.
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl. 2014(2014):38.
E. Karapinar, B. Samet, Generalized (α,Ψ)-contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal. 2012(2012), Article ID 793486.
E. Karapinar, Interpolative Kannan-Meir-Keeler type contraction Advances in the Theory of Nonlinear Analysis and its Application, 5(4)(2021), 611-614.
E. Karapinar, A. Fulga, S. S. Yesilkaya, New Results on Perov-Interpolative Contractions of Suzuki Type Mappings, Journal of Function Spaces, Volume 2021, Article ID 9587604, 7 pages.
E. Karapinar, R. P. Agarwal, Interpolative Rus-Reich-Ćirić type contractions via simulation functions, Analele Universitatii Ovidius 27(2019), 137-152.
Karapinar, E Agarwal, R. Aydi, H. Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics, 6(11), (2018), 256.
E. Karapinar, A. Fulga, A. F. R. L. de Hierro, Fixed point theory in the setting of (α, β, ψ, ϕ)-interpolative contractions, AIDE, 2021:339(2021), 1-16.
E. Karapinar, H. Aydi, A. Fulga, On-hybrid Wardowski contractions, Journal of Mathematics, Volume 2020, Article ID 1632526, 8 pages.
E. Karapinar, A. Fulga, New hybrid contractions on b-metric spaces, Mathematics, 7(7)(2019), 578.
E. Karapinar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl., 2 (2018), 85-87.
E. Karapinar, O. Alqahtani, H. Aydi, On Interpolative Hardy-Rogers Type Contractions, Symmetry 2019, 11, 8.
E. Karapinar, H. Aydi, Z. D. Mitrović, On interpolative Boyd-Wong and Matkowski type contractions, TWMS J. Pure Appl. Math. 11(2) (2020), 204-212.
M. S. Khan, Y. M. Singh, E. Karapinar, On the Interpolative (φ,ψ)-Type Z-Contraction, U.P.B. Sci. Bull., Series A, Vol. 83(2021), 25-38.
Z. Li, S. Jiang, Fixed point theorems of JS-quasi-contractions, Fixed Point Theory Appl. 2016:40 (2016).
A. Lukács, S. Kajánto, Fixed point theorems for various types of F-contractions in complete b-metric spaces, Fixed Point Theory, 19(2018), 321-334.
J. Matkowski, Integrable solutions of functional equations, Diss. Math. 127(1975), 1-68.
S. Moradi, Fixed point of single-valued cyclic weak φF-contraction mappings, Filomat 28 (2014), 1747-1752.
M. Nazam, C. Park, M. Arshad, Fixed point problems for generalized contractions with applications, Advances in Difference Equations 2021(2021):247, https://doi.org/10.1186/s13662-021-03405-w.
M. Nazam, H. Aydi, A. Hussain, Generalized Interpolative Contractions and an Application, Journal of Mathematics, 2021(2021), Article ID 6461477.
L. Pasick, The Boyd-Wong idea extended, Fixed Point Theory and Applications (2016) 2016:63, doi 10.1186/s13663-016-0553-0.
P. D. Proinov, Fixed point theorems for generalized contractive mappings in metric spaces, J. Fixed Point Theory Appl. (2020) 22:21, https://doi.org/10.1007/s11784-020-0756-1.
E. Rakotch, A note on contractive mappings, Proc. Am. Math. Soc. 13(1962), 459-465.
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Am. Math. Soc. 132(2003), 1435-1443.
T. Rasham, A. Shoaib, B. A. S. Alamri, M. Arshad, Multivalued fixed point results for new generalized F-dominated contractive mappings on dislocated metric space with application, J. Funct. Spaces, 2018 (2018), Article ID 4808764, 12 pages.
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for (α,ψ)-contractive type mappings, Nonlinear Anal. 75(2012), 2154-2165.
N. A. Secelean, Weak F-contractions and some fixed point results, Bull. Iranian Math. Soc. 42(2016), 779-798.
F. Skof, Theoremi di punto fisso per applicazioni negli spazi metrici, Atti. Acad. Sci. Torino Cl. Sci. Fis. Mat. Natur. 111(1977), 323-329.
D. Wardowski, Solving existence problems via F-contractions, Proc. Am. Math. Soc. 146(2017), 1585-1598.
D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces, Fixed Point Theory Appl. (2012) Article ID 94.