In this paper, the term "Bicomplex valued extended b-metric spaces" or briefly "BC-valued extended b-metric spaces" refers to a new extension of bicomplex valued b-metric spaces that we introduce in this study. Using this novel class of metric spaces, we extend numerous findings from literature and establish fixed point theorems with the aid of illustrative examples. Moreover, as an application of our results, we show that a unique solution of the Urysohn integral exists.
In this work, we present a numerical algorithm for approaching the solutions of a specific form of linear and nonlinear Fredholm integro-differential equations. This algorithm is constructed by applying the weighted integral mean value methods, which allow us to convert the proposed equations into a system of algebraic equations, then by solving this system we obtain the approximate solutions. Moreover, we provide some illustrative examples to show the effectiveness and simplicity of the algorithm.
In this paper, we investigate some theorems on the existence and convergence of best proximity point for a semi-cyclic contraction pair (S, T) in the setting of non solid cone E-metric space with empty interior containing semi-interior points which poses larger class of metric spaces. further we apply our finding results in the E-cone metric space to prove the existence of the solution of certain integral equation.
Image compression is crucial for reducing the size of digital images, particularly in applications such as medical imaging and satellite communication. Discrete Wavelet Transform (DWT) has emerged as a powerful tool for image compression due to its multiresolution analysis capabilities. In this study, we propose a novel thresholding technique for selecting optimal threshold values to enhance image compression using DWT. We evaluate the performance of our approach using different wavelets, including Haar, db2, db5, sym2, and coif1, and analyze key metrics such as Peak Signal-to-Noise Ratio (PSNR), Compression Score (CS), and L-2-norm recovery. Here, we show that for first level of decomposition using db2 wavelet, our proposed technique achieves a PSNR of 35.79 dB, a CS of 75%, and an L-2-norm recovery of 99.946% when applied to a standard 474 & times; 474 image of Srinivasa Ramanujan. Our method not only maintains image quality but reduces computational time compared to existing thresholding techniques. This work contributes to the advancement of efficient image compression techniques in various domains.
The homomorphic image of a fuzzy module over an R-module is itself a fuzzy module, yet explicit bounds on level cardinalities under specific structural constraints remain largely unexplored. In prior work, such bounds were established for Z-module homomorphisms Gamma : Z(m)-> Z(n) when gcd(m, n) is either a prime or the product of two distinct primes, getting maxima of 3 and 4 respectively. In this paper, we extend these results to the cases gcd(m, n) = p(s), where p is a prime and s is an element of Z(+) and further to the case gcd(m, n) = p(1)(s1) .p(s2) (2) ... p(k)(st) , with distinct primes p(i )and s(i) is an element of Z(+), i = 1,2,. . .t. Our results contribute to a deeper understanding of the behavior of fuzzy modules under structural mappings between cyclic modules.
