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COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS BY A MODIFIED FASTER ITERATION SCHEME
Khan, Safeer Hussain,Kim, Jong-Kyu Korean Mathematical Society 2010 대한수학회보 Vol.47 No.5
We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand, it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme, we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.
COMMON FIXED POINTS OF TWO NONEXPANSIVE MAPPINGS BY A MODIFIED FASTER ITERATION SCHEME
Safeer Hussain Khan,김종규 대한수학회 2010 대한수학회보 Vol.47 No.5
We introduce an iteration scheme for approximating common fixed points of two mappings. On one hand, it extends a scheme due to Agarwal et al. [2] to the case of two mappings while on the other hand,it is faster than both the Ishikawa type scheme and the one studied by Yao and Chen [18] for the purpose in some sense. Using this scheme,we prove some weak and strong convergence results for approximating common fixed points of two nonexpansive self mappings. We also outline the proofs of these results to the case of nonexpansive nonself mappings.
Safeer Hussain Khan,Ritika,Vishnu Narayan Mishra 한국전산응용수학회 2021 Journal of Applied and Pure Mathematics Vol.3 No.1
CAT(0) spaces contain a number of spaces including both linear and nonlinear ones. The class of generalized asymptotically quasi-nonexpansive mappings is a very wide class of mappings. Iterative processes are used to approximate solutions when actual one is hard to find. In this paper, we prove strong convergence results using a three step iterative process for generalized asymptotically quasi-nonexpansive mappings in CAT(0) spaces. Our results remain valid in both linear and nonlinear domains. Thus our results generalize the corresponding results of many authors.
Mujahid Abbas,Safeer Hussain Khan,김종규 영남수학회 2010 East Asian mathematical journal Vol.26 No.5
We study one-step iteration process to approximate common fixed points of two nonexpansive mappings and prove some convergence theorems in convex metric spaces. Using the so-called condition (A′), the convergence of iteratively defined sequences in a uniformly convex metric space is also obtained.
Effects of elastic medium on buckling of microtubules due to bending and torsion
Taj, Muhammad,Hussain, Muzamal,Afsar, Muhammad A.,Safeer, Muhammad,Ahmad, Manzoor,Naeem, Muhammad N.,Badshah, Noor,Khan, Arshad,Tounsi, Abdelouahed Techno-Press 2020 Advances in concrete construction Vol.9 No.5
Microtubules buckle under bending and torsion and this property has been studied for free microtubules before using orthotropic elastic shell model. But as microtubules are embedded in other elastic filaments and it is experimentally showed that these elastic filaments affect the critical buckling moment and critical buckling torque of the microtubules. To prove that, we developed orthotropic Winkler like model and demonstrated that the critical buckling moment and critical buckling torque of the microtubules are orders of higher magnitude than those found for free microtubules. Our results show that Critical buckling moment is about 6.04 nNnm for which the corresponding curvature is about θ = 1.33 rad /㎛ for embedded MTs, and critical buckling torque is 0.9 nNnm for the angle of 1.33 rad/㎛. Our results well proved the experimental findings.
Abbas, Mujahid,Khan, Safeer Hussain,Kim, Jong-Kyu The Youngnam Mathematical Society Korea 2010 East Asian mathematical journal Vol.26 No.5
We study one-step iteration process to approximate common fixed points of two nonexpansive mappings and prove some convergence theorems in convex metric spaces. Using the so-called condition (A'), the convergence of iteratively defined sequences in a uniformly convex metric space is also obtained.
Muhammad Taj,Muhammad Safeer,Muzamal Hussain,Muhammad N. Naeem,Manzoor Ahmad,Kamran Abbas,Abdul Q. Khan,Abdelouahed Tounsi 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.25 No.3
Cytoskeleton components in living cell bear large compressive force and are responsible in maintaining the cell shape. Actually these filaments are surrounded by viscoelastic media within the cell. This surrounding, viscoelastic media affects the buckling behavior of these filaments when external force is applied on these filaments by exerting continuous pressure in opposite directions to the incipient buckling of the filaments. In this article a mechanical model is applied to account the effects of this media on the buckling behavior of intermediate filaments network of cytoskeleton. The model immeasurably associates; filament’s bending rigidity, adjacent system elasticity, and cytosol viscosity with buckling wavelength, buckling growth rate and buckling amplitude of the filaments.
Non-local orthotropic elastic shell model for vibration analysis of protein microtubules
Muhammad Taj,Afnan Majeed,Muzamal Hussain,Muhammad N. Naeem,Muhammad Safeer,Manzoor Ahmad,Hidayat Ullah Khan,Abdelouahed Tounsi 사단법인 한국계산역학회 2020 Computers and Concrete, An International Journal Vol.25 No.3
Vibrational analysis in microtubules is examined based on the nonlocal theory of elasticity. The complete analytical formulas for wave velocity are obtained and the results reveal that the small scale effects can reduce the frequency, especially for large longitudinal wave-vector and large circumferential wave number. It is seen that the small scale effects are more significant for smaller wave length. The methods and results may also support the design and application of nano devices such as micro sound generator etc. The effects of small scale parameters can increase vibrational frequencies of the protein microtubules and cannot be overlooked in the analysis of vibrating phenomena. The results for different modes with nonlocal effect are checked.
Mechanics of anisotropic cardiac muscles embedded in viscoelastic medium
Taj, Muhammad,Khadimallah, Mohamed Amine,Hussain, Muzamal,Ghandourah, E.,Safeer, Muhammad,Elbahar, Mohamed,Khan, Manzoor,Elimame, Elaloui Techno-Press 2021 Advances in concrete construction Vol.12 No.1
In the present work the author incorporated the surrounding medium with Hodgkin Huxley model to account the effect of surroundings on the flow of current in cardiac muscles fibers. The Hodgkin Huxley Kelvin like model is developed here and then the governing equations are solved by appropriate mathematical methods and the obtained results are compared with the previous experimental findings. Through obtained solutions, we check the mechanical properties in actual environment of cardiac muscles fibres and compare our findings with experimental results. Previous Hodgkin Huxley model did not give any idea about the medium, in which the cardiac muscles are immersed. The new developed model accounts the effect of medium efficiently on the current flow along with fiber's stimulation in cardiac muscles.