COINCIDENCE THEOREMS VIA CONTRACTIVE MAPPINGS IN ORDERED NON-ARCHIMEDEAN FUZZY METRIC SPACES
2
조회
0
다운로드
1
인용
0
참고문헌
키워드
초록
In this article, we prove coincidence point theorems for comparable ψ-contractive mappings in ordered non-Archimedean fuzzy metric spaces utilizing the recently established concept of T -comparability and relatively weaker order theoretic variants. With a view to show the usefulness and applicability of this work, we solve the system of ordered Fredholm integral equations as an application. In the process, this presentation generalize and improve some prominent recent results obtained in Mihet [Fuzzy Sets Syst., 159 (6), 739-744, (2008)], Altun and Mihet [ Fixed Point Theory Appl. 2010, 782680, (2010)], Alam and Imdad [Fixed Point Theory, 18(2), 415-432, (2017)] and several others in the settings of partially ordered non-Archimedean fuzzy metric spaces.
Abstract
In this article, we prove coincidence point theorems for comparable ψ-contractive mappings in ordered non-Archimedean fuzzy metric spaces utilizing the recently established concept of T -comparability and relatively weaker order theoretic variants. With a view to show the usefulness and applicability of this work, we solve the system of ordered Fredholm integral equations as an application. In the process, this presentation generalize and improve some prominent recent results obtained in Mihet [Fuzzy Sets Syst., 159 (6), 739-744, (2008)], Altun and Mihet [ Fixed Point Theory Appl. 2010, 782680, (2010)], Alam and Imdad [Fixed Point Theory, 18(2), 415-432, (2017)] and several others in the settings of partially ordered non-Archimedean fuzzy metric spaces.
참고문헌 (26)
- A. Alam, "Comparable linear contractions in ordered metric spaces", Fixed Point Theory, 18(2), pp.415~432 (2017)
- Aftab Alam, "Monotone generalized contractions in ordered metric spaces", 대한수학회보, 53(1), pp.61~81 (2016), 대한수학회
- I. Altun, "Ordered non-Archimedean fuzzy metric spaces and some fixed point results", Fixed Point Theory Appl, 2010 (2010)
- I. Altun, "Some fixed point theorems for single and multi valued mappings on ordered non-Archimedean fuzzy metric spaces", Iran. J. Fuzzy Syst., 7(1), pp.91~96 (2010)
- Ramesh Chandra Dimri, "Coincidence theorems for comparable generalized non linear contractions in ordered partial metric spaces", 대한수학회논문집, 32(2), pp.375~387 (2017), 대한수학회
- A. George, "On some results in fuzzy metric spaces", Fuzzy Sets Syst, 64(3), pp.395~399 (1994)
- K. Goebel, "A coincidence theorem", Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys., 16, pp.733~735 (1968)
- M. Grabiec, "Fixed points in fuzzy metric spaces", Fuzzy Sets Syst, 27(3), pp.385~389 (1988)
- V. Gregori, "Contractive sequences in fuzzy metric spaces", Fuzzy Sets Syst., 379, pp.125~133 (2020)
- V. Gregori, "On fuzzy Ψ-contractive sequences and fixed point theorems", Fuzzy Sets Syst, 300, pp.93~101 (2016)
- V. Istratescu, "An Introduction to Theory of Probabilistic Metric Spaces with Applica-tions" (1974), Ed, Tehnica
- R.H. Haghi, "Some fixed point generalizations are not real generalizations", Nonlinear Anal. :Theory, Method and Appl., 74(5), pp.1799~1803 (2011)
- G. Jungck, "Fixed points for set valued functions without continuity", Indian J. Pure Appl. Math., 29(3), pp.227~238 (1998)
- I. Kramosil, "Fuzzy metrics and statistical metric spaces", Kybernetika, 11(5), pp.336~344 (1975)
- S. Lipschutz, "Schaum's Outlines of Theory and Problems of Set Theory and Related Topics" (1964), McGraw-Hill
- D. Mihet, "Fuzzy Ψ-contractive mappings in non-Archimedean fuzzy metric spaces", Fuzzy Sets Syst, 159(6), pp.739~744 (2008)
- S.N. Mishra, "Common fixed points of maps on fuzzy metric spaces", Int. J. Math. Math. Sci., 17(2), pp.253~258 (1994)
- J.J. Nieto, "Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations", Order, 22, pp.223~239 (2005)
- R.P. Pant, "A common fixed point theorem under a new condition", Indian J. Pure Appl. Math., 30, pp.147~152 (1999)
- G. Prasad, "Fixed point theorems via comparable mappings in ordered metric spaces", J. Anal, 27(4), pp.1139~1150 (2019)
- A.C M. Ran, "A fixed point theorem in partially ordered sets and some applications to matrix equations", Proc. Amer. Math. Soc., 132(5), pp.1435~1443 (2003)
- B. Said, "Integral type common fixed point theorems in modified intu-itionistic fuzzy metric spaces", Afr. Math., 30, pp.581~596 (2019)
- B. Schweizer, "Statistical metric spaces", Pac. J. Math., 10, pp.313~334 (1960)
- S. L. Singh, "Fixed point theorems in FM-spaces", Fuzzy Mathematics, 12(4), pp.845~859 (2004)
- M. Turinici, "Fixed points for monotone iteratively local contractions", Demonstr. Math., 19(1), pp.171~180 (1986)
- M. Turinici, "Ran-Reurings fixed point results in ordered metric spaces", Libertas Math, 31, pp.49~55 (2011)