An application of the w-weak generalized contractions theorem
Article
First Online:
- 123 Downloads
Abstract
Using the w-weak generalized contractions theorem of Wongyat and Sintunavarat (Adv Diff Equ 2017:211, 2017) and their idea to apply this theorem to the nonlinear integral equations to obtain an existence and uniqueness result, in this paper we present another application of this theorem to a nonlinear Fredholm integral equation with modified argument, which completes the study of this equation.
Keywords
w-Distance altering distance function ceiling distance nonlinear Fredholm integral equation modified argument solution existence and uniquenessMathematics Subject Classification
Primary 47H10 Secondary 45G10Notes
References
- 1.Aguirre Salazar, L., Reich, S.: A remark on weakly contractive mappings. J. Nonlinear Convex Anal. 16, 767–773 (2015)MathSciNetzbMATHGoogle Scholar
- 2.Alegre, C., Marin, J., Romaguera, S.: A fixed point theorem for generalized contractions involving w-distances on complete quasi-metric spaces. Fixed Point theory Appl. 2014, 40 (2014)MathSciNetCrossRefGoogle Scholar
- 3.Ambro, M.: Approximation of the solutions of an integral equation with modified argument. Studia Univ. Babeş-Bolyai Math. 2, 26–32 (1978). (in Romanian)MathSciNetzbMATHGoogle Scholar
- 4.Choudhury, B.S., Konar, P., Rhoades, B.E., Metyia, N.: Fixed point theorems for generalized weakly contractive mapping. Nonlinear Anal. 74(6), 2116–2126 (2011)MathSciNetCrossRefGoogle Scholar
- 5.Dobriţoiu, M.: An integral equation with modified argument. Studia Univ. Babeş-Bolyai Math. XLIX(3), 27–34 (2004)MathSciNetzbMATHGoogle Scholar
- 6.Dobriţoiu, M.: On an integral equation with modified argument. Acta Universitatis Apulensis, Mathematics-Informatics 11, 387–391 (2006)MathSciNetzbMATHGoogle Scholar
- 7.Dobriţoiu, M.: Analysis of an integral equation with modified argument. Studia Univ. Babeş-Bolyai Math. 51(1), 81–94 (2006)MathSciNetzbMATHGoogle Scholar
- 8.Dobriţoiu, M.: Analysis of a Nonlinear Integral Equation with Modified Argument from Physics. Int. J. Math. Models Methods Appl. Sci. (NAUN Electron. J.) 2(3), 403–412 (2008)Google Scholar
- 9.Dobriţoiu, M.: Integral Equations with Modifed Argument. Cluj University Press, Cluj-Napoca (2009). (in Romanian)Google Scholar
- 10.Dobriţoiu, M.: A nonlinear Fredholm integral equation. Transylv. J. Math. Mech. 1(1–2), 25–32 (2009)MathSciNetGoogle Scholar
- 11.Ilea, V., Otrocol, D.: Some properties of solutions of a functional-differential equation of second order with delay. Sci. World J. 2014, 878395 (2014). https://doi.org/10.1155/2014/878395 CrossRefzbMATHGoogle Scholar
- 12.Lakzian, H., Aydi, H., Rhoades, B.E.: Fixed points for \((\phi,\psi,\rho )\)-weakly contractive mappings in metric spaces with w-distance. Appl. Math. Comput. 219(12), 6777–6782 (2013)MathSciNetzbMATHGoogle Scholar
- 13.Rus, I.A.: Weakly Picard operators and applications. Semin Fixed Point Theory Babeş-Bolyai Univ Cluj-Napoca 2, 41–58 (2001)MathSciNetzbMATHGoogle Scholar
- 14.Rus, I.A.: Principii şi aplicaţii ale teoriei punctului fix. Editura Dacia, Cluj-Napoca (1979). (in Romanian)Google Scholar
- 15.Wongyat, T., Sintunavarat, W.: The existence and uniqueness of the solution for nonlinear Fredholm and Volterra integral equations together with nonlinear fractional differential equations via w-distances. Adv. Diff. Equ. 2017, 211 (2017)MathSciNetCrossRefGoogle Scholar
Copyright information
© Springer Nature Switzerland AG 2019