Utilizing Generalized Meir-Keeler Contraction in Periodic Boundary Value Problems
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This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir- Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.
Abstract
This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir- Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.
참고문헌 (18)
- S. A. Al-Mezel, "Discussion on multidimen-sional coincidence points via recent publications", Abstr. Appl. Anal, 2014 (2014)
- V. Berinde, "Coupled xed point theorems for generalized symmetric Meir-Keeler contractions in ordered metric spaces", Fixed Point Theory Appl, pp.115~ (2012)
- T.G. Bhaskar, "Fixed point theorems in partially ordered metric spaces and applications", Nonlinear Anal, 65(7), pp.1379~1393 (2006)
- B.S. Choudhury, "A coupled coincidence point results in partially ordered metric spaces for compatible mappings", Nonlinear Anal, 73, pp.2524~2531 (2010)
- B.S. Choudhury, "A generalized weak contraction principle with applications to coupled coincidence point problems", Fixed Point Theory Appl, pp.152~ (2013)
- B. Deshpande, "Coincidence point results for weak contraction on partially ordered metric spaces with application", Facta Universitatis Ser. Math. Inform, 30(5), pp.623~648 (2015)
- B. Deshpande, "On coincidence point theorem for new contractive condition with application", Facta Universitatis Ser. Math. Inform, 32(2), pp.209~229 (2017)
- B. Deshpande, "Coincidence point theorem under Mizoguchi-Takahashi contraction on ordered metric spaces with application", Int. J. Math. Appl, 3(4-A), pp.75~94 (2015)
- Bhavana Deshpande, "HUGE CONTRACTION ON PARTIALLY ORDERED METRIC SPACES", 순수 및 응용수학, 23(1), pp.35~51 (2016), 한국수학교육학회
- I.M. Erhan, "Remarks on coupled coincidence point results for a generalized compatible pair with applications", Fixed Point Theory Appl, pp.207~ (2014)
- D. Guo, "Coupled xed points of nonlinear operators with ap-plications", Nonlinear Anal, 11(5), pp.623~632 (1987)
- A. Handa, "Coincidence point results for contrac-tion mapping principle on partially ordered metric spaces with application to ordinary differential equations", Adalaya Journal, 8(9), pp.734~754 (2019)
- G. Jungck, "Compatible mappings and common xed points", Internat. J. Math. & Math. Sci, 9(4), pp.771~779 (1986)
- G. Jungck, "Fixed point for set-valued functions without continuity", Indian J. Pure Appl. Math, 29(3), pp.227~238 (1998)
- V. Lakshmikantham, "Coupled xed point theorems for nonlinear contrac-tions in partially ordered metric spaces", Nonlinear Anal, 70(12), pp.4341~4349 (2009)
- A. Meir, "A theorem on contraction mappings", J. Math. Anal. Appl, 28, pp.326~329 (1969)
- B. Samet, "Coupled xed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces", Nonlinear Anal, 72, pp.4508~4517 (2010)
- B. Samet, "Discussion on some coupled xed point theorems", Fixed Point Theory Appl, pp.50~ (2013)
