Research Article
Year 2023,
Volume: 7 Issue: 1, 29 - 40, 31.03.2023
Abstract
We initiate the use of sub and super homogeneous control functions for nonlinear contractions in complete metric spaces and establish new fixed point theorems. Moreover, we develop other variants of control functions for the fixed point theorems of Boyd-Wong [2] and Matkowski [3]. As application, we present new sufficient conditions ensuring the existence of solutions to some classes of integral equations of Fredholm and Volterra type.
References
- S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., vol. 3, no. 1, pp. 133-181, 1922.
- D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., vol. 20, no. 2, pp. 458--464, 1969.
- J. Matkowski, Integrable solutions of functional equations, Dissertationes Math., pp. 1--68, 1975.
- Reference4 J. Jachymski, Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., vol. 125, no. 8, pp. 2327--2335, 1997.
- J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces, Nonlinear Anal., vol. 74, no. 3, pp. 768--774, 2011.
- R. P. Agarwal, E. Karapinar, D. O'Regan, and A. F. Roldan-Lopez-de Hierro, Fixed point theory in metric type spaces. Springer, 2015.
- J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., vol. 62, no. 2, pp. 344--348, 1977.
- K.-J. Chung, Remarks on nonlinear contractions, Pacific J. Math., vol. 101, no. 1, pp. 41--48, 1982.
- D. O'Regan and A. Petrucel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., vol. 341, no. 2, pp. 1241--1252, 2008.
- M. Sgroi and C. Vetro, Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat, vol. 27, no. 7, pp. 1259--1268, 2013.
Year 2023,
Volume: 7 Issue: 1, 29 - 40, 31.03.2023
Abstract
References
- S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math., vol. 3, no. 1, pp. 133-181, 1922.
- D. W. Boyd and J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., vol. 20, no. 2, pp. 458--464, 1969.
- J. Matkowski, Integrable solutions of functional equations, Dissertationes Math., pp. 1--68, 1975.
- Reference4 J. Jachymski, Equivalence of some contractivity properties over metrical structures, Proc. Amer. Math. Soc., vol. 125, no. 8, pp. 2327--2335, 1997.
- J. Jachymski, Equivalent conditions for generalized contractions on (ordered) metric spaces, Nonlinear Anal., vol. 74, no. 3, pp. 768--774, 2011.
- R. P. Agarwal, E. Karapinar, D. O'Regan, and A. F. Roldan-Lopez-de Hierro, Fixed point theory in metric type spaces. Springer, 2015.
- J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., vol. 62, no. 2, pp. 344--348, 1977.
- K.-J. Chung, Remarks on nonlinear contractions, Pacific J. Math., vol. 101, no. 1, pp. 41--48, 1982.
- D. O'Regan and A. Petrucel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., vol. 341, no. 2, pp. 1241--1252, 2008.
- M. Sgroi and C. Vetro, Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat, vol. 27, no. 7, pp. 1259--1268, 2013.
There are 10 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Articles |
| Authors | |
| Publication Date | March 31, 2023 |
| Published in Issue | Year 2023 Volume: 7 Issue: 1 |