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Nashine, Hemant Kumar,Kadelburg, Zoran,Agarwal, Ravi P. Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.4
We present ${\alpha}$-type rational F-contractions in metric-like spaces, and respective fixed and common fixed point results for weakly ${\alpha}$-admissible mappings. Useful examples illustrate the effectiveness of the presented results. As applications, we obtain sufficient conditions for the existence of solutions of a certain type of integral equations followed by examples of nonlinear fractional differential equations that are verified numerically.
COMMON FIXED POINT THEOREM AND INVARIANT APPROXIMATION IN COMPLETE LINEAR METRIC SPACES
Nashine, Hemant Kumar The Youngnam Mathematical Society 2012 East Asian mathematical journal Vol.28 No.5
A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.
Nashine, Hemant Kumar,Kadelburg, Zoran Korean Mathematical Society 2015 대한수학회보 Vol.52 No.3
We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.
Nashine, Hemant Kumar,Gupta, Anita The Youngnam Mathematical Society 2016 East Asian mathematical journal Vol.32 No.5
We propose coupled fixed point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces. We also present a result on the existence and uniqueness of coupled fixed points. In particular, it is shown that the results existing in the literature are extend, generalized, unify and improved by using mixed monotone property. Given to support the useability of our results, and to distinguish them from the known ones.
COMMON FIXED POINTS AND INVARIANT APPROXIMATIONS FOR SUBCOMPATIBLE MAPPINGS IN CONVEX METRIC SPACE
Nashine, Hemant Kumar,Kim, Jong-Kyu The Youngnam Mathematical Society 2010 East Asian mathematical journal Vol.26 No.1
Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.
Best Approximation Result in Locally Convex Space
NASHINE, HEMANT KUMAR 대한수학회 2006 Kyungpook mathematical journal Vol.46 No.3
A fixed point theorem of Singh and Singh [10] is generalized to locally convex spaces and the new result is applied to extend a result on invariant approximation of Jungck and Sessa [5].
Hemant Kumar Nashine,Rabha W. Ibrahim,Yeol Je Cho,Jong Kyu Kim 경남대학교 수학교육과 2021 Nonlinear Functional Analysis and Applications Vol.26 No.1
In this paper, first, we prove some common fixed point theorems for the generalized contraction condition under newly defined modified simulation function which generalize and include many results in the literature. Second, we give two numerical examples with graphical representations for verifying the proposed results. Third, we discuss and study a set of common fixed point theorems for two pairs (finite families) of self-mappings. Fi- nally, we give some applications of our results in discrete and functional fractional economic systems.
Hemant Kumar Nashine,Anita Gupta 영남수학회 2016 East Asian mathematical journal Vol.32 No.5
We propose coupled fixed point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces. We also present a result on the existence and uniqueness of coupled fixed points. In particular, it is shown that the results existing in the literature are extend, generalized, unify and improved by using mixed monotone property. Given to support the useability of our results, and to distinguish them from the known ones.
CONTROL FUNCTION BASED COUPLED AND COMMON COUPLED FIXED POINT THEOREMS IN PARTIAL METRIC SPACES
H. K. Nashine,G.S. Saluja,G. V. V. J. Rao,W. H. Lim 경남대학교 수학교육과 2024 Nonlinear Functional Analysis and Applications Vol.29 No.2
In this paper, we aim to prove coupled and common coupled fixed point theorems for contractive type conditions in the context of partial metric spaces by means of a control function, and to provide some corollaries of the established results. This paper presents a number of results that generalize and extend previous work in the field. In order to better illustrate the process, we provide examples.
COMMON FIXED POINTS AND INVARIANT APPROXIMATIONS FOR SUBCOMPATIBLE MAPPINGS IN CONVEX METRIC SPACE
Hemant Kumar Nashine,김종규 영남수학회 2010 East Asian mathematical journal Vol.26 No.1
Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex metric spaces have been obtained. Invariant approximation results have also been derived by its application. These results extend and generalize various known results in the literature with the aid of more general class of noncommuting mappings.