• Nonlinear Functional Analysis and Applications
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• v.27 no.3
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• pp.449-469
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• 2022

This paper deals with the new iterative algorithm for approximating the fixed point of generalized 𝛼-nonexpansive mappings in a hyperbolic space. We show that the proposed iterative algorithm is faster than all of Picard, Mann, Ishikawa, Noor, Agarwal, Abbas, Thakur and Piri iteration processes for contractive mappings in a Banach space. We also establish some weak and strong convergence theorems for generalized 𝛼-nonexpansive mappings in hyperbolic space. The examples and numerical results are provided in this paper for supporting our main results.

• Journal of Broadcast Engineering
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• v.4 no.1
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• pp.76-85
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• 1999

The degradation of image quality by block loss is more serious in fractal coded images with the error propagation due to mapping from the lost blocks than in DCT coded images. Therefore. a new algorithm is presented for recovering the blocks lost in the transmission through the lossy network as A TM network of the images coded by Jacquins fractal coding. Jacquins fractal code is divided into two layers of header code and main code according to its importance. The key technique of the proposed BLRA (block loss recovery algorithm) is a fractal extrapolation that estimates the lost pixels by using the contractive mapping parameters of the neighboring range blocks whose characteristics are similar to a lost block. The proposed BLRA is applied to the lost blocks in the iteration of decoding. Some experimental results show the proposed BLRA yields excellent performance in PSNR as well as subjective quality.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.247-257
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• 1997

It was the turning point in the "fixed point arena" when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in "Fixed Point Theory and its Application in various other Branches of Mathematical Sciences" in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called "compatibility" of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.

• Journal of the Institute of Convergence Signal Processing
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• v.3 no.1
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• pp.41-47
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• 2002

Fractal image compression can reduce the size of image data by the contractive mapping that is affine transformation to find the block(called as range block) which is the most similar to the original image. Even though fractal image compression is regarded as an efficient way to reduce the data size, it has high distortion rate and requires long encoding time. In this paper, we presented a hybrid fractal image compression system with the modified SOFM Vector Quantizer which uses improved competitive learning method. The simulation results showed that the VQ hybrid fractal using improved competitive loaming SOFM has better distortion rate than the VQ hybrid fractal using normal SOFM.