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UNIFYING A MULTITUDE OF COMMON FIXED POINT THEOREMS EMPLOYING AN IMPLICIT RELATION
Ali, Javid,Imdad, Mohammad Korean Mathematical Society 2009 대한수학회논문집 Vol.24 No.1
A general common fixed point theorem for two pairs of weakly compatible mappings using an implicit function is proved without any continuity requirement which generalizes the result due to Popa [20, Theorem 3]. In process, several previously known results due to Fisher, Kannan, Jeong and Rhoades, Imdad and Ali, Imdad and Khan, Khan, Shahzad and others are derived as special cases. Some related results and illustrative examples are also discussed. As an application of our main result, we prove an existence theorem for the solution of simultaneous Hammerstein type integral equations.
A GENERAL FIXED POINT THEOREM IN FUZZY METRIC SPACES VIA AN IMPLICIT FUNCTION
Imdad, M.,Ali, Javid Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
We employ the notion of implicit functions to prove a general common fixed point theorem in fuzzy metric spaces besides adopting the idea of R-weak commutativity of type (P) in fuzzy setting. In process, several previously known results are deduced as special cases to our main result.
Railway Track Structural Health Monitoring System
Fatima Imdad,Muhammad Tabish Niaz,Hyung Seok Kim 제어로봇시스템학회 2015 제어로봇시스템학회 국제학술대회 논문집 Vol.2015 No.10
Railway is one of the most used means of transportation. For the railway system to operate flawlessly constant monitoring and inspection of railway tracks is required. Currently railway track inspection and monitoring is done manually which is time taking and not accurate, due to the high chance of human error occurrence. Moreover, practically it is impossible to inspect and monitor the railway track manually as they run thousands of miles. To avoid this we propose a prototype system, designed for continuous monitoring of railway tracks using a combination of sensors. These sensors collect data and through computational analysis faults in the railway tracks are identified. The collected data can help in finding cracks in the tracks and catastrophic accidents can be avoided.
A general fixed point theorem in fuzzy metric spaces via an implicit function
M. Imdad,Javid Ali 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.3-4
We employ the notion of implicit functions to prove a general common fixed point theorem in fuzzy metric spaces besides adopting the idea of R-weak commutativity of type (P) in fuzzy setting. In process, several previously known results are deduced as special cases to our main result. We employ the notion of implicit functions to prove a general common fixed point theorem in fuzzy metric spaces besides adopting the idea of R-weak commutativity of type (P) in fuzzy setting. In process, several previously known results are deduced as special cases to our main result.
Mohammad Imdad,Waleed M. Alfaqih 경남대학교 기초과학연구소 2018 Nonlinear Functional Analysis and Applications Vol.23 No.1
The aim of this paper is to prove some unified common fixed point theoremsunder contractive conditions of integral type for two pairs of weakly compatible mappings satisfying the property (E.A) in complex valued symmetric spaces using an implicit relation. Some illustrative examples are also given which substantiate the usefulness of our utilized implicit relation. Our results generalize and improve some of the existing results in theliterature and at the same time deduce new contractions of integral type in the context of complex fixed point theory. We apply one of our results to examine the existence and uniqueness of common solution for a system of Volterra-Hammerstein integral equations.
윤용석,Imdad Ullah Khan,최경욱,정태성,조광래,이수형,김완희,김대용,권오경 한국조직공학과 재생의학회 2018 조직공학과 재생의학 Vol.15 No.1
Cell sheets technology is being available for fracture healing. This study was performed to clarify bone healing mechanism of undifferentiated (UCS) and osteogenic (OCS) differentiated mesenchymal stromal cell (MSC) sheets in the fracture model of dogs. UCS and OCS were harvested at 10 days of culture. Transverse fractures at the radius of six beagle dogs were assigned into three groups (n = 4 in each group) i.e. UCS, OCS and control. The fractures were fixed with a 2.7 mm locking plate and six screws. Cell sheets were wrapped around the fracture site. Bones were harvested 8 weeks after operation, then scanned by micro-computed tomography (micro-CT) and analyzed histopathologically. The micro-CT revealed different aspects of bone regeneration among the groups. The percentages of external callus volume out of total bone volume in control, UCS, and OCS groups were 42.1, 13.0 and 4.9% (p\0.05) respectively. However, the percentages of limbs having connectivity of gaps were 25, 12.5 and 75% respectively. In histopathological assessments, OCS group showed well organized and mature woven bone with peripheral cartilage at the fracture site, whereas control group showed cartilage formation without bone maturation or ossification at the fracture site. Meanwhile, fracture site was only filled with fibrous connective tissue without endochondral ossification and bone formation in UCS group. It was suggested that the MSC sheets reduced the quantity of external callus, and OCS induced the primary bone healing.
A NEW ITERATION SCHEME FOR A HYBRID PAIR OF NONEXPANSIVE MAPPINGS
Uddin, Izhar,Imdad, Mohammad The Honam Mathematical Society 2016 호남수학학술지 Vol.38 No.1
In this paper, we construct an iteration scheme involving a hybrid pair of nonexpansive mappings and utilize the same to prove some convergence theorems. In process, we remove a restricted condition (called end-point condition) in Sokhuma and Kaewkhao's results [Sokhuma and Kaewkhao, Fixed Point Theory Appl. 2010, Art. ID 618767, 9 pp.].
MONOTONE GENERALIZED CONTRACTIONS IN ORDERED METRIC SPACES
Alam, Aftab,Imdad, Mohammad Korean Mathematical Society 2016 대한수학회보 Vol.53 No.1
In this paper, we prove some existence and uniqueness results on coincidence points for g-monotone mappings satisfying linear as well as generalized nonlinear contractivity conditions in ordered metric spaces. Our results generalize and extend two classical and well known results due to Ran and Reurings (Proc. Amer. Math. Soc. 132 (2004), no. 5, 1435-1443) and Nieto and $Rodr{\acute{i}}guez$-$L{\acute{o}}pez$ (Acta Math. Sin. 23 (2007), no. 12, 2205-2212) besides similar other ones. Finally, as an application of one of our newly proved results, we establish the existence and uniqueness of solution of a first order periodic boundary value problem.