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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.
Vishal Nikam,Dhananjay Gopal,Habib ur Rehman,Thanatporn Bantaojai 경남대학교 기초과학연구소 2020 Nonlinear Functional Analysis and Applications Vol.25 No.4
The true motivation of this article is to provide sucient conditions with theaid of Geraghty type condensing operators that guarantee the existence of a solution of non-linear quadratic Volterra-Stieltjes integral equation. We also address several new fixed pointtheorems that ensure the existence of a xed point for Geraghty type condensing operatorsin real Banach spaces. An example and numerical approximations are presented to justifythe basis of our results.
ON APPLICATIONS OF GENERALIZED F-CONTRACTION TO DIFFERENTIAL EQUATIONS
Younis Mudasir,Singh Deepak,Gopal Dhananjay,Goyal Anil,Rathore Mahendra Singh 경남대학교 기초과학연구소 2019 Nonlinear Functional Analysis and Applications Vol.24 No.1
In the present work, we introduce the new concept of a generalization of Ger- aghty type F-Berinde contraction mappings and establish certain existence results for such mappings. Some examples will embellish the results, for the same computer simulation is done. Our examples involve a series of complicated structured functions which cannot be treated by classical fixed point methods. Our findings extend, unify and enrich a multitude results in the existing literature. As an application, we apply our abstract results to establish the existence of solution of differential equations of first and second order to exhibit the po- tency and viability of our results. At the end, as an open problem, we suggest storekeeper’s control problem in terms of Volterra integral equation whose solution may be procured from the established results.