Best Proximity Point Results in Fuzzy Normed Spaces
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Keywords:
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Fuzzy Normed Space, Fuzzy Proximal Contractive, Best Proximity Point, Fuzzy Banach Space, Cauchy Sequence
Abstract
Fixed point (briefly FP ) theory is a potent tool for resolving several actual problems since many problems may be simplified to the FP problem. The idea of Banach contraction mapping is a foundational theorem in FP theory. This idea has wide applications in several fields; hence, it has been developed in numerous ways. Nevertheless, all of these results are reliant on the existence and uniqueness of a FP on some suitable space. Because the FP problem could not have a solution in the case of nonself-mappings, the idea of the best proximity point (briefly Bpp) is offered to approach the best solution. This paper investigates the existence and uniqueness of the Bpp of nonself-mappings in fuzzy normed space(briefly FN space) to arrive at the best solution. Following the introduction of the definition of the Bpp, the existence, and uniqueness of the Bpp are shown in a FN space for diverse fuzzy proximal contractions such as ?????? fuzzy proximal contractive mapping and ????h ????h - fuzzy proximal contractive mapping.
References
Abbas, M., V. Parvaneh, and A. Razani (2012). Periodic Points of T-Ciric Generalized Contraction Mappings in Ordered Metric Spaces. Georgian Mathematical Journal, 19(4); 597–610
Bag, T. and S. Samanta (2003). Finite Dimensional Fuzzy Normed Linear Spaces. Journal of Fuzzy Mathematics, 11(3); 687–706
Banach, S. (1922). Sur Les Opérations Dans Les Ensembles Abstraits Et Leur Application Aux équations Intégrales. Fundamenta Mathematicae, 3(1); 133–181
Dakheel, S. O. and B. A. Ahmed (2021). On C 1 C 2 Symmetric Operators. Journal of Interdisciplinary Mathematics, 24(7); 1965–1971
Eiman, H. A. and A.Mustafa (2016). On Some Generalizations of n,m -normal Powers Operators on Hilbert Space. Journal of Progressive Research in Mathematics, 7(3); 34–38
George, A. and P. Veeramani (1994). On Some Results in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 64(3); 395–399
Gregori, V., J.-J. Miñana, and D. Miravet (2020). Contractive Sequences in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 379; 125–133
Guria, S., P. Saha, and B. S. Choudury (2019). Determining Fuzzy Distance Through Non-self Fuzzy Contractions. Yugoslav Journal of Operations Research, 29(3); 325–335
Hussain, N., H. H. Al sulami, and G. Ali (2020). Best Proximity Point Results for Theta-contraction in Modular Metric and Fuzzy Metric Spaces. Bulletin of Mathematical Analysis & Applications, 12(4); 1–14
Kider, J. R. and N. Kadhum (2019). Properties of Fuzzy Closed Linear Operator. Engineering and Technology Journal, 37(01 Part B); 25–31
Konwar, N. and P. Debnath (2023). Theory of Approximation for Operators in Intuitionistic Fuzzy Normed Linear Spaces. Sequence Space Theory with Applications; 139–153
Kramosil, I. and J. Michálek (1975). Fuzzy Metrics and Statistical Metric Spaces. Kybernetika, 11(5); 336–344
Latif, A., V. Parvaneh, P. Salimi, and A. Al Mazrooei (2015). Various Suzuki Type Theorems in B Metric Spaces. Journal Nonlinear Science Application, 8(4); 363–377
Li, C. and Y. Zhang (2023). On P-Convergent Sequences and p-Cauchy Sequences in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 12(2); 20–25
Lin, G., X. Cheng, and Y. Zhang (2018). A Parametric Level Set Based Collage Method for an Inverse Problem in Elliptic Partial Differential Equations. Journal of Computational and Applied Mathematics, 340; 101–121
Miheţ, D. and C. Zaharia (2014). A Note on the Definition of a Generalized Fuzzy Normed Space. Fuzzy Sets and Systems, 238; 129–134
Mustafa, Z., J. R. Roshan, V. Parvaneh, and Z. Kadelburg (2014). Fixed Point Theorems for Weakly T-Chatterjea and Weakly T-Kannan Contractions in b-Metric Spaces. Journal of Inequalities and Applications, 2014; 1–14
Nadaban, S. and I. Dzitac (2014). Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications. Informatica, 25(4); 643–662
Nemah, E. M. (2017). Modified Iterative Solution of Nonlinear Uniformly Continuous Mappings Equation in Arbitrary Real Banach Space. Ibn AL Haitham Journal For Pure and Applied Science, 26(3); 379–386
Paknazar, M. (2018). Non-Archimedean Fuzzy Metric Spaces and Best Proximity Point Theorems. Sahand Communications in Mathematical Analysis, 9(1); 85–112
Raghad, S. (2021). Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces. Baghdad Science Journal, 18(4); 1204–1204
Sabre, R. I. (2012). Product of Two Fuzzy Normed Spaces and Its Completion. Engineering and Technology Journal, 30(11); 1925–1934
Sabri, R. I. (2021). Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function. Iraqi Journal of Science, 62(9); 3031–3038
Sabri, R. I. and B. A. Ahmed (2022). Best Proximity Point Results for Generalization of aˆ-nˆ Proximal Contractive Mapping in Fuzzy Banach Spaces. Indonesian Journal of Electrical Engineering and Computer Science, 28(3); 1451–1462
Sabri, R. I. and B. A. Ahmed (2023). Best Proximity Point Theorem for Contractive Type Mapping in Fuzzy Normed Space. Baghdad Science Journal, 3(4); 15–20
Sharma, M. and D. Hazarika (2020). Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and Its Fuzzy Compactness. New Mathematics and Natural Computation, 16(01); 177–193
Zadeh, L. A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1(1); 3–28
Zainab, A. and J. Kider (2021). The Hausdorff Algebra Fuzzy Distance and its Basic Properties. Engineering and Technology Journal, 39(7); 1185–1194
Zeana, Z. J. and K.Assma (2016). Data Dependence Result And Stability Of Picard-S Iteration Scheme For Approximating Fixed Point Of Almost Contraction Mappings. International Journal of Advanced Research, 4(5); 760–763
Zhang, Y. and B. Hofmann (2020). Two New Non-negativity Preserving Iterative Regularization Methods for Ill-posed Inverse Problems. Inverse Problem Image, 2(15); 229–256
Bag, T. and S. Samanta (2003). Finite Dimensional Fuzzy Normed Linear Spaces. Journal of Fuzzy Mathematics, 11(3); 687–706
Banach, S. (1922). Sur Les Opérations Dans Les Ensembles Abstraits Et Leur Application Aux équations Intégrales. Fundamenta Mathematicae, 3(1); 133–181
Dakheel, S. O. and B. A. Ahmed (2021). On C 1 C 2 Symmetric Operators. Journal of Interdisciplinary Mathematics, 24(7); 1965–1971
Eiman, H. A. and A.Mustafa (2016). On Some Generalizations of n,m -normal Powers Operators on Hilbert Space. Journal of Progressive Research in Mathematics, 7(3); 34–38
George, A. and P. Veeramani (1994). On Some Results in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 64(3); 395–399
Gregori, V., J.-J. Miñana, and D. Miravet (2020). Contractive Sequences in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 379; 125–133
Guria, S., P. Saha, and B. S. Choudury (2019). Determining Fuzzy Distance Through Non-self Fuzzy Contractions. Yugoslav Journal of Operations Research, 29(3); 325–335
Hussain, N., H. H. Al sulami, and G. Ali (2020). Best Proximity Point Results for Theta-contraction in Modular Metric and Fuzzy Metric Spaces. Bulletin of Mathematical Analysis & Applications, 12(4); 1–14
Kider, J. R. and N. Kadhum (2019). Properties of Fuzzy Closed Linear Operator. Engineering and Technology Journal, 37(01 Part B); 25–31
Konwar, N. and P. Debnath (2023). Theory of Approximation for Operators in Intuitionistic Fuzzy Normed Linear Spaces. Sequence Space Theory with Applications; 139–153
Kramosil, I. and J. Michálek (1975). Fuzzy Metrics and Statistical Metric Spaces. Kybernetika, 11(5); 336–344
Latif, A., V. Parvaneh, P. Salimi, and A. Al Mazrooei (2015). Various Suzuki Type Theorems in B Metric Spaces. Journal Nonlinear Science Application, 8(4); 363–377
Li, C. and Y. Zhang (2023). On P-Convergent Sequences and p-Cauchy Sequences in Fuzzy Metric Spaces. Fuzzy Sets and Systems, 12(2); 20–25
Lin, G., X. Cheng, and Y. Zhang (2018). A Parametric Level Set Based Collage Method for an Inverse Problem in Elliptic Partial Differential Equations. Journal of Computational and Applied Mathematics, 340; 101–121
Miheţ, D. and C. Zaharia (2014). A Note on the Definition of a Generalized Fuzzy Normed Space. Fuzzy Sets and Systems, 238; 129–134
Mustafa, Z., J. R. Roshan, V. Parvaneh, and Z. Kadelburg (2014). Fixed Point Theorems for Weakly T-Chatterjea and Weakly T-Kannan Contractions in b-Metric Spaces. Journal of Inequalities and Applications, 2014; 1–14
Nadaban, S. and I. Dzitac (2014). Atomic Decompositions of Fuzzy Normed Linear Spaces for Wavelet Applications. Informatica, 25(4); 643–662
Nemah, E. M. (2017). Modified Iterative Solution of Nonlinear Uniformly Continuous Mappings Equation in Arbitrary Real Banach Space. Ibn AL Haitham Journal For Pure and Applied Science, 26(3); 379–386
Paknazar, M. (2018). Non-Archimedean Fuzzy Metric Spaces and Best Proximity Point Theorems. Sahand Communications in Mathematical Analysis, 9(1); 85–112
Raghad, S. (2021). Fuzzy Convergence Sequence and Fuzzy Compact Operators on Standard Fuzzy Normed Spaces. Baghdad Science Journal, 18(4); 1204–1204
Sabre, R. I. (2012). Product of Two Fuzzy Normed Spaces and Its Completion. Engineering and Technology Journal, 30(11); 1925–1934
Sabri, R. I. (2021). Compactness Property of Fuzzy Soft Metric Space and Fuzzy Soft Continuous Function. Iraqi Journal of Science, 62(9); 3031–3038
Sabri, R. I. and B. A. Ahmed (2022). Best Proximity Point Results for Generalization of aˆ-nˆ Proximal Contractive Mapping in Fuzzy Banach Spaces. Indonesian Journal of Electrical Engineering and Computer Science, 28(3); 1451–1462
Sabri, R. I. and B. A. Ahmed (2023). Best Proximity Point Theorem for Contractive Type Mapping in Fuzzy Normed Space. Baghdad Science Journal, 3(4); 15–20
Sharma, M. and D. Hazarika (2020). Fuzzy Bounded Linear Operator in Fuzzy Normed Linear Spaces and Its Fuzzy Compactness. New Mathematics and Natural Computation, 16(01); 177–193
Zadeh, L. A. (1978). Fuzzy Sets as a Basis for a Theory of Possibility. Fuzzy Sets and Systems, 1(1); 3–28
Zainab, A. and J. Kider (2021). The Hausdorff Algebra Fuzzy Distance and its Basic Properties. Engineering and Technology Journal, 39(7); 1185–1194
Zeana, Z. J. and K.Assma (2016). Data Dependence Result And Stability Of Picard-S Iteration Scheme For Approximating Fixed Point Of Almost Contraction Mappings. International Journal of Advanced Research, 4(5); 760–763
Zhang, Y. and B. Hofmann (2020). Two New Non-negativity Preserving Iterative Regularization Methods for Ill-posed Inverse Problems. Inverse Problem Image, 2(15); 229–256
Authors
Sabri, R. I. ., & Ahmed, B. A. A. H. . (2023). Best Proximity Point Results in Fuzzy Normed Spaces. Science and Technology Indonesia, 8(2), 298–304. https://doi.org/10.26554/sti.2023.8.2.298-304
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