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2022 | OriginalPaper | Buchkapitel

Perturbed Geometric Contractions in Ordered Metric Spaces

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Abstract

A geometric extension is given for the perturbed contraction principle in Aydi et al. [Abstr. Appl. Anal., Volume 2013, Article ID 312479].

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Literatur
1.
Zurück zum Zitat R.P. Agarwal, M.A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces. Appl. Anal. 87, 109–116 (2008)MathSciNetMATHCrossRef R.P. Agarwal, M.A. El-Gebeily, D. O’Regan, Generalized contractions in partially ordered metric spaces. Appl. Anal. 87, 109–116 (2008)MathSciNetMATHCrossRef
2.
Zurück zum Zitat H. Aydi, S.H. Amor, E. Karapinar, Berinde-type generalized contractions on partial metric spaces. Abstr. Appl. Anal. 2013, 312479 (2013)MathSciNetMATH H. Aydi, S.H. Amor, E. Karapinar, Berinde-type generalized contractions on partial metric spaces. Abstr. Appl. Anal. 2013, 312479 (2013)MathSciNetMATH
3.
Zurück zum Zitat S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 3, 133–181 (1922)MathSciNetCrossRefMATH S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math. 3, 133–181 (1922)MathSciNetCrossRefMATH
4.
Zurück zum Zitat V. Berinde, Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9, 43–53 (2004)MathSciNetMATH V. Berinde, Approximating fixed points of weak contractions using the Picard iteration. Nonlinear Anal. Forum 9, 43–53 (2004)MathSciNetMATH
5.
Zurück zum Zitat P. Bernays, A system of axiomatic set theory. Part III: Infinity and enumerability analysis. J. Symbol. Logic 7, 65–89 (1942)MathSciNetMATH P. Bernays, A system of axiomatic set theory. Part III: Infinity and enumerability analysis. J. Symbol. Logic 7, 65–89 (1942)MathSciNetMATH
7.
Zurück zum Zitat I. Cabrera, J. Harjani, K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces. Ann. Univ. Ferrara 59, 251–258 (2013)MathSciNetMATHCrossRef I. Cabrera, J. Harjani, K. Sadarangani, A fixed point theorem for contractions of rational type in partially ordered metric spaces. Ann. Univ. Ferrara 59, 251–258 (2013)MathSciNetMATHCrossRef
8.
Zurück zum Zitat S. Chandok, B.S. Choudhury, N. Metiya, Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions. J. Egypt. Math. Soc. 23, 95–101 (2015)MathSciNetMATHCrossRef S. Chandok, B.S. Choudhury, N. Metiya, Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions. J. Egypt. Math. Soc. 23, 95–101 (2015)MathSciNetMATHCrossRef
9.
Zurück zum Zitat B.S. Choudhury, N. Metiya, Fixed point theorems for almost contractions in partially ordered metric spaces. Ann. Univ. Ferrara 58, 21–36 (2012)MathSciNetMATHCrossRef B.S. Choudhury, N. Metiya, Fixed point theorems for almost contractions in partially ordered metric spaces. Ann. Univ. Ferrara 58, 21–36 (2012)MathSciNetMATHCrossRef
10.
Zurück zum Zitat L.B. Cirić, A new fixed-point theorem for contractive mappings. Publ. Inst. Math. 30(44), 25–27 (1981)MathSciNetMATH L.B. Cirić, A new fixed-point theorem for contractive mappings. Publ. Inst. Math. 30(44), 25–27 (1981)MathSciNetMATH
11.
Zurück zum Zitat P.J. Cohen, Set Theory and the Continuum Hypothesis (Benjamin, New York, 1966)MATH P.J. Cohen, Set Theory and the Continuum Hypothesis (Benjamin, New York, 1966)MATH
12.
Zurück zum Zitat P. Collaco, J.C. E Silva, A complete comparison of 25 contractive definitions. Nonlinear Anal. 30, 441–476 (1997) P. Collaco, J.C. E Silva, A complete comparison of 25 contractive definitions. Nonlinear Anal. 30, 441–476 (1997)
13.
Zurück zum Zitat C. Di Bari, C. Vetro, Common fixed point theorems for weakly compatible maps satisfying a general contractive condition. Int. J. Math. Math. Sci. 2008, 891375 (2008)MathSciNetMATH C. Di Bari, C. Vetro, Common fixed point theorems for weakly compatible maps satisfying a general contractive condition. Int. J. Math. Math. Sci. 2008, 891375 (2008)MathSciNetMATH
14.
Zurück zum Zitat P.N. Dutta, B.S. Choudhury, A generalisation of contraction principle in metric spaces. Fixed Point Theory Appl. 2008, 406368 (2008)MathSciNetMATHCrossRef P.N. Dutta, B.S. Choudhury, A generalisation of contraction principle in metric spaces. Fixed Point Theory Appl. 2008, 406368 (2008)MathSciNetMATHCrossRef
16.
Zurück zum Zitat P.R. Halmos, Naive Set Theory (Van Nostrand Reinhold, New York, 1960)MATH P.R. Halmos, Naive Set Theory (Van Nostrand Reinhold, New York, 1960)MATH
17.
Zurück zum Zitat P. Hitzler, Generalized metrics and topology in logic programming semantics. Ph.D. Thesis, National University of Ireland, University College Cork (2001) P. Hitzler, Generalized metrics and topology in logic programming semantics. Ph.D. Thesis, National University of Ireland, University College Cork (2001)
18.
Zurück zum Zitat J. Jachymski, Common fixed point theorems for some families of mappings. Ind. J. Pure Appl. Math. 25, 925–937 (1994)MathSciNetMATH J. Jachymski, Common fixed point theorems for some families of mappings. Ind. J. Pure Appl. Math. 25, 925–937 (1994)MathSciNetMATH
19.
Zurück zum Zitat J. Jachymski, The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc. 136, 1359–1373 (1994)MathSciNetMATHCrossRef J. Jachymski, The contraction principle for mappings on a metric space with a graph. Proc. Am. Math. Soc. 136, 1359–1373 (1994)MathSciNetMATHCrossRef
20.
Zurück zum Zitat J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Anal. 74, 768–774 (2011)MathSciNetMATHCrossRef J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Anal. 74, 768–774 (2011)MathSciNetMATHCrossRef
22.
Zurück zum Zitat S. Kasahara, On some generalizations of the Banach contraction theorem. Publ. Res. Inst. Math. Sci. Kyoto Univ. 12, 427–437 (1976)MathSciNetMATHCrossRef S. Kasahara, On some generalizations of the Banach contraction theorem. Publ. Res. Inst. Math. Sci. Kyoto Univ. 12, 427–437 (1976)MathSciNetMATHCrossRef
23.
Zurück zum Zitat M.S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points. Bull. Austral. Math. Soc. 30, 1–9 (1984)MathSciNetMATHCrossRef M.S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points. Bull. Austral. Math. Soc. 30, 1–9 (1984)MathSciNetMATHCrossRef
24.
Zurück zum Zitat S. Leader, Fixed points for general contractions in metric spaces. Math. Japonica 24, 17–24 (1979)MathSciNetMATH S. Leader, Fixed points for general contractions in metric spaces. Math. Japonica 24, 17–24 (1979)MathSciNetMATH
25.
Zurück zum Zitat J. Matkowski, Integrable solutions of functional equations. Dissert. Math., vol. 127, (Polish Scientific Publishers, Warsaw, 1975) J. Matkowski, Integrable solutions of functional equations. Dissert. Math., vol. 127, (Polish Scientific Publishers, Warsaw, 1975)
26.
Zurück zum Zitat J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point. Proc. Am. Math. Soc. 62, 344–348 (1977)MathSciNetMATHCrossRef J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point. Proc. Am. Math. Soc. 62, 344–348 (1977)MathSciNetMATHCrossRef
27.
29.
Zurück zum Zitat G.H. Moore, Zermelo’s Axiom of Choice: Its Origin, Development and Influence (Springer, New York, 1982)MATHCrossRef G.H. Moore, Zermelo’s Axiom of Choice: Its Origin, Development and Influence (Springer, New York, 1982)MATHCrossRef
30.
Zurück zum Zitat Y. Moskhovakis, Notes on Set Theory (Springer, New York, 2006) Y. Moskhovakis, Notes on Set Theory (Springer, New York, 2006)
32.
Zurück zum Zitat J.J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223–239 (2005)MathSciNetMATHCrossRef J.J. Nieto, R. Rodriguez-Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22, 223–239 (2005)MathSciNetMATHCrossRef
33.
Zurück zum Zitat A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2004)MathSciNetMATHCrossRef A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2004)MathSciNetMATHCrossRef
34.
35.
37.
Zurück zum Zitat I.A. Rus, Generalized Contractions and Applications (Cluj University Press, Cluj-Napoca, 2001)MATH I.A. Rus, Generalized Contractions and Applications (Cluj University Press, Cluj-Napoca, 2001)MATH
38.
Zurück zum Zitat B. Samet, M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications. Commun. Math. Anal. 13, 82–97 (2012)MathSciNetMATH B. Samet, M. Turinici, Fixed point theorems on a metric space endowed with an arbitrary binary relation and applications. Commun. Math. Anal. 13, 82–97 (2012)MathSciNetMATH
39.
Zurück zum Zitat E. Schechter, Handbook of Analysis and its Foundation (Academic Press, New York, 1997)MATH E. Schechter, Handbook of Analysis and its Foundation (Academic Press, New York, 1997)MATH
41.
Zurück zum Zitat M. Turinici, Fixed points of implicit contraction mappings. An. Şt. Univ. “Al. I. Cuza” Iaşi (S I-a, Mat), 22, 177–180 (1976) M. Turinici, Fixed points of implicit contraction mappings. An. Şt. Univ. “Al. I. Cuza” Iaşi (S I-a, Mat), 22, 177–180 (1976)
42.
Zurück zum Zitat M. Turinici, Nonlinear contractions and applications to Volterra functional equations. An. Şt. Univ. “Al. I. Cuza” Iaşi (S I-a, Mat) 23, 43–50 (1977) M. Turinici, Nonlinear contractions and applications to Volterra functional equations. An. Şt. Univ. “Al. I. Cuza” Iaşi (S I-a, Mat) 23, 43–50 (1977)
43.
Zurück zum Zitat M. Turinici, Fixed points for monotone iteratively local contractions. Dem. Math. 19, 171–180 (1986)MathSciNetMATH M. Turinici, Fixed points for monotone iteratively local contractions. Dem. Math. 19, 171–180 (1986)MathSciNetMATH
44.
Zurück zum Zitat M. Turinici, Abstract comparison principles and multivariable Gronwall-Bellman inequalities. J. Math. Anal. Appl. 117, 100–127 (1986)MathSciNetMATHCrossRef M. Turinici, Abstract comparison principles and multivariable Gronwall-Bellman inequalities. J. Math. Anal. Appl. 117, 100–127 (1986)MathSciNetMATHCrossRef
45.
Zurück zum Zitat M. Turinici, Function pseudometric VP and applications. Bul. Inst. Polit. Iaşi (S. Mat., Mec. Teor., Fiz.) 53(57), 393–411 (2007) M. Turinici, Function pseudometric VP and applications. Bul. Inst. Polit. Iaşi (S. Mat., Mec. Teor., Fiz.) 53(57), 393–411 (2007)
46.
Zurück zum Zitat M. Turinici, Ran-Reurings theorems in ordered metric spaces. J. Indian Math. Soc. 78, 207–214 (2011)MathSciNetMATH M. Turinici, Ran-Reurings theorems in ordered metric spaces. J. Indian Math. Soc. 78, 207–214 (2011)MathSciNetMATH
47.
Zurück zum Zitat M. Turinici, Rational contractions and coupled fixed points, in Applications of Nonlinear Analysis ed. by T.M. Rassias, chap. 26 (Springer, Basel, 2018), pp. 781–825 M. Turinici, Rational contractions and coupled fixed points, in Applications of Nonlinear Analysis ed. by T.M. Rassias, chap. 26 (Springer, Basel, 2018), pp. 781–825
48.
49.
Zurück zum Zitat R.N. Yadava, R. Shrivastava, S.S. Yadav, Rational type contraction mapping in T-orbitally complete metric space. Math. Theory Model. 4, 115–133 (2014) R.N. Yadava, R. Shrivastava, S.S. Yadav, Rational type contraction mapping in T-orbitally complete metric space. Math. Theory Model. 4, 115–133 (2014)
Metadaten
Titel
Perturbed Geometric Contractions in Ordered Metric Spaces
verfasst von
Mihai Turinici
Copyright-Jahr
2022
DOI
https://doi.org/10.1007/978-3-030-84122-5_42