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C*-algebra valued symmetric spaces and fixed point results with an application
Mohammad Asim,Mohammad Imdad 강원경기수학회 2020 한국수학논문집 Vol.28 No.1
In this paper, we firstly introduce the class of $C^*$-algebra valued symmetric spaces and utilize the same to prove our fixed point results. We furnish an example to highlight the utility of our main result. Finally, we apply our result to examine the existence and uniqueness of a solution for a system of Fredholm integral equations.
Mohammad Imdad,Waleed M. Alfaqih 경남대학교 수학교육과 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.
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 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.
A NEW ITERATION SCHEME FOR A HYBRID PAIR OF NONEXPANSIVE MAPPINGS
( Izhar Uddin ),( Mohammad Imdad ) 호남수학회 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
Aftab Alam,Mohammad Imdad 대한수학회 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. {\bf 132} (2004), no. 5, 1435--1443) and Nieto and Rodr\'{\i}guez-L\'{o}pez (Acta Math. Sin. {\bf 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.
PROVING UNIFIED COMMON FIXED POINT THEOREMS VIA COMMON PROPERTY (E-A) IN SYMMETRIC SPACES
Soliman, Ahmed Hussein,Imdad, Mohammad,Hasan, Mohammad Korean Mathematical Society 2010 대한수학회논문집 Vol.25 No.4
A metrical common fixed point theorem proved for a pair of self mappings due to Sastry and Murthy ([16]) is extended to symmetric spaces which in turn unifies certain fixed point theorems due to Pant ([13]) and Cho et al. ([4]) besides deriving some related results. Some illustrative examples to highlight the realized improvements are also furnished.
REMARKS ON CERTAIN NOTED COINCIDENCE THEOREMS: A UNIFYING AND ENRICHING APPROACH
Aftab Alam,Mohd. Hasan,Mohammad Imdad 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.5
In this paper, we unify and enrich the well-known classical metrical coincidence theorems on a complete metric space due to Machuca, Goebel and Jungck. We further extend our newly proved results on a subspace Y of metric space X, wherein X need not be complete. Finally, we slightly modify the existing results involving (E.A)-property and (CLR_g)-property and apply these results to deduce our coincidence and common fixed point theorems.
Gopal, Dhananjay,Hasan, Mohammad,Imdad, Mohammad Korean Mathematical Society 2012 대한수학회논문집 Vol.27 No.2
The purpose of this paper is to improve certain results proved in a recent paper of Soliman et al. [20]. These results are the outcome of utilizing the idea of absorbing pairs due to Gopal et al. [6] as opposed to two conditions namely: weak compatibility and the peculiar condition initiated by Pant [15] to ascertain the common fixed points of Lipschitzian mappings. Some illustrative examples are also furnished to highlight the realized improvements.