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( Surjeet Singh Chauhan ),( Kiran Utreja ),( Mohammad Imdad ),( Md Ahmadullah ) 호남수학회 2017 호남수학학술지 Vol.39 No.1
In this paper, we introduce a new scheme namely: CUIA- iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.
Chauhan, Surjeet Singh,Utreja, Kiran,Imdad, Mohammad,Ahmadullah, Md The Honam Mathematical Society 2017 호남수학학술지 Vol.39 No.1
In this paper, we introduce a new scheme namely: CUIA-iterative scheme and utilize the same to prove a strong convergence theorem for quasi contractive mappings in Banach spaces. We also establish the equivalence of our new iterative scheme with various iterative schemes namely: Picard, Mann, Ishikawa, Agarwal et al., Noor, SP, CR etc for quasi contractive mappings besides carrying out a comparative study of rate of convergences of involve iterative schemes. The present new iterative scheme converges faster than above mentioned iterative schemes whose detailed comparison carried out with the help of different tables and graphs prepared with the help of MATLAB.
Geraghty type contractions in $b-$metric-like spaces
Surjeet Singh Chauhan(Gonder),Kanika Rana,Mohammad Imdad 강원경기수학회 2022 한국수학논문집 Vol.30 No.4
The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in $b-$metric-like spaces, which remains an extended version of corresponding results in $b-$metric spaces and metric-like spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in $b-$metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in $b-$metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.
COUPLED FIXED POINT THEOREMS FOR RATIONAL INEQUALITY IN GENERALIZED METRIC SPACES
Singh, Deepak,Tomar, Surjeet Singh,Rathore, M.S.,Chauhan, Varsha The Youngnam Mathematical Society 2015 East Asian mathematical journal Vol.31 No.1
In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.
Coupled fixed point theorems for rational inequality in generalized metric spaces
Deepak Singh,Surjeet Singh Tomar,M.S.Rathore,Varsha Chauhan 영남수학회 2015 East Asian mathematical journal Vol.31 No.1
In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G- metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.