DOI: 10.12732/ijam.v37i3.3
A NOVEL APPROACH FOR SOME FIXED POINT RESULTS
IN COMPLETE G-METRIC SPACE BY USING
ASYMPTOTICALLY REGULAR MAPPING
IN DIGITAL IMAGE COMPRESSION AND
DECOMPRESSION APPLICATIONS
R. Anna Thirumalai 1, S. Thalapathiraj 2,§
1,2 Department of Mathematics
Faculty of Engineering and Technology
SRM Institute of Science and Technology
Vadapalani Campus
No.1 Jawaharlal Nehru Salai, Vadapalani
Chennai - 26, Tamil Nadu, INDIA
Abstract. In this paper, we extend some unique fixed point theorem results on a complete symmetric G-metric space by using asymptotically regular mappings with a new approach. Moreover, the new structure of extended G-contractive mapping on suitable spaces is used to create images with reduced size in this paper. A digital image is a representation of two-dimensional pixels arrays. A mild but typical system of extended G-contractive mapping on the Euclidean plane, known as the digital plane, is implemented for image processing to produce images with compressed dimensions that take up less storage space and can be transmitted efficiently. The size of the initial picture matrix has been reduced dramatically on decreasing the order of sub-matrices, resulting in images of reduced size with little loss in image quality. When images are enlarge and appeared in a short screen, the variations between the original and reduced image are not as noticeable (mobile, tablets, etc.)
How
to cite this paper?
DOI: 10.12732/ijam.v37i3.3
Source: International Journal of Applied Mathematics
ISSN printed version: 1311-1728
ISSN on-line version: 1314-8060
Year: 2024
Volume: 37
Issue: 3
References
[1] S. Banach, Sur les operations dans les ensembles abstraits et leurs applications
aux equations integrales, Fund. Math., 3 (1922), 133-181.
[2] S. Gahler, 2-Metrices Raume und Ihre Topologische Struktur, Mathematische
Nachrichten, 26 (1963), 115-148.
[3] B. C. Dhage, Generalized Metric Spaces and Mappings with Fixed Point,
Bulletin of Calcutta Mathematical Society, 84 (1992), 329-336.
[4] Z. Mustafa, B. Sims, Some remarks concerninig d-metric spaces, Proceeding
of the International Conferences on Fixed Point Theory and Applications, (2003), 189-198.
[5] Z. Mustafa, B. Sims, A new approach to generalized metric spaces, Journal of Nonlinear and Convex Analysis, 7 (2006), 287-297.
[6] A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 33 (2011), 243-253.
[7] L. Boxer, Digitally continuous functions, Pattern Recognit. Lett., 15 (1994), 833-839.
[8] F. E. Browder and W. V. Petryshyn, The solution by iteration of non linear functional equations in banach spaces, Bull. Amer. Math. Soc., 72 (1966), 571–575.
[9] O. Ege, I. Karaca, Fundamental properties of simplicial homology groups for digital images, American Journal of Computer Technology and Application, 1 (2013), 25-42.
[10] O. Ege, I. Karaca, Banach fixed point theorem for digital images, J. Nonlinear Sci. Appl., 8 (2015), 237-245.
[11] R. Anna Thirumalai, S. Thalapathiraj, A novel approach for digital image compression in some fixed point results on complete G-metric space using comparison function, Int. J. Anal. Appl., 21 (2023), 110.
[12] S. Thalapathiraj, B. Baskaran, J. Arunnehru, A block based secret sharing scheme using Hilbert matrix and RSA, AIP Conference Proceedings, 2112 (2019).
[13] P. Bosilj, E. Kijak, S. Lef‘evre, Partition and inclusion hierarchies of images: a comprehensive survey, J. Imaging., 33 (2018).
[14] S. E. Han, Banach fixed point theorem from the viewpoint of digital topology, J. Nonlinear Sci. Appl., 9 (2016), 895-905.
[15] S. E. Han, Connected sum of digital closed surfaces, Inform. Sci., 176 (2006), 332-348.
[16] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. App., 332 (2007), 1468-1476.
[17] M. Jleli, B. Samet, Remarks on g-metric spaces and fixed point theorems, Fixed Point Theory Appl., 2012 (2012).
[18] I. Karaca, O. Ege, Some results on simplicial homology groups of 2D digital images. Int. J. Inform. Computer Sci., 1(2012), 198-203.
[19] A. Rosenfeld, Digital topology, Amer. Math. Mon., 86 (1979).
[20] G. Prasad, R. C. Dimri, Fixed point theorems via comparable mappings in ordered metric spaces, J. Anal., 27 (2019), 1139-1150.
[21] Durdana Lateef, Fisher type fixed point results in controlled metric spaces, J. Math. Computer Sci., 20 (2020), 234-240.
[22] R. Anna Thirumalai, S. Thalapathiraj, Solution of the boundary value problems via fixed point theorem on G-metric space, IAENG International Journal of Applied Mathematics, 53 (2023), 1357-1369.
[23] K Hemavathy, S. Thalapathiraj, Common Fixed Point Theorems for 2-Metric Space using Various EA Properties, IAENG International Journal of Applied Mathematics, 53 (2023), 1-7.
[24] R. Anna Thirumalai, S. Thalapathiraj, C. Rajesh, Some common fixed point results in complete G-metric space by using four mappings, AIP Conf. Proc., 2852 (2023).
[25] A. El Haddouchi, B. Marzouki, A generalized fixed point theorem in G-metric space, Journal of Analysis and Applications, 17 (2019), 89-105.
[26] K. H. Thung, P. Raveendran, A survey of image quality measures, International
Conference for Technical Postgraduates (TECHPOS), (2009), 1-4.
[27] Samjhana Koirala, Narayan Prasad Pahari, Some results on fixed point theory in G-metric space, International Journal of Mathematics Trends and Technology, 67 (2021), 150-156.
[28] Narinder Kumar, Manoj Kumar, Ashish, Fixed point theory for simulation functions in G-metric spaces: A novel approach, Advances in Fixed Point Theory, 12 (2022), 9 pages.
[29] Budi Nurwahyu, Naimah Aris, Firman, Some results in function weighted b-metric spaces, AIMS Mathematics, 8 (2023), 8274-8293.
[30] Deepthi K. Oommen, J. Arunnehru, Alzheimer’s disease stage classification using a deep transfer learning and sparse auto encoder method, Computers, Materials and Continua, 76 (2023), 793-811.
[31] Deepthi K. Oommen, J. Arunnehru, Detection and classification of Alzheimer’s Disease: A deep learning approach with predictor variables, Diagnosis of Neurological Disorders Based on Deep Learning Techniques, (2023), 85-98.
[32] R. Rajkumar, J. Arunnehru, A study on convolutional neural networks with active video tubelets for object detection and classification, Soft Computing and Signal Processing: Proceedings of ICSCSP 2018 (2019), 107-115.
(c) 2024, Diogenes Co, Ltd.; https://www.diogenes.bg/ijam/