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Sumit Chandok

Guru Nanak Dev University Amritsar, Department of Mathematics, Alumnus

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IBN ZOHR UNIVERSITY

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Southern Illinois University Edwardsville

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Viatcheslav Melas

Ithaya Ezhil Manna

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Papers by Sumit Chandok

Some approximate fixed point results and application on graph theory for partial (h-F)-generalized convex contraction mappings with special class of functions on complete metric space

In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgenerali... more In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgeneralized) convex contractions of order 3 (and with rank 3) using some auxiliary functions. Also we present some approximate fixed point results in metric space and approximate fixed point results in metric space endowed with a graph. Some examples are provided to illustrate the main results and to show the essentiality of the given hypotheses.

Generalized Krasnoselskii fixed point theorem involving auxiliary functions in bimetric spaces and application to two-point boundary value problem

In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary funct... more In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary functions, and obtained some sufficient conditions for existence and uniqueness of fixed point for such mappings on bimetric spaces. We also establish a result on coincidence point of two mappings, and derive several corollaries of our main theorems. As application, we establish an existence result for a two-point boundary value problem of second order differential equation.

Common fixed points and invariant approximation of R -subweakly commuting maps in convex metric spaces

Ukrainian Mathematical Journal, 2011

Sufficient conditions for the existence of a common fixed point of R-subweakly commuting mappings... more Sufficient conditions for the existence of a common fixed point of R-subweakly commuting mappings are established within the framework of a convex metric space. As applications, we obtain various results on the best approximation for this class of mappings generalizing the results known from the literature.

Some common fixed point theorems for generalized nonlinear contractive mappings

Computers & Mathematics With Applications, 2011

In this paper, we first prove a common fixed point theorem for generalized nonlinear contraction ... more

Some Common Fixed Point Results for generalized weak contractive Mappings in Partially Ordered Metric Spaces

Page 1. SOME COMMON FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTIVE MAPPINGS IN PARTIALLY OR... more

Common Fixed Points and Invariant Approximations for Cq-commuting Generalized Nonexpansive Mappings

Abstract. Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings hav... more Abstract. Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings have been proved in metric spaces. As applications, invariant approximation results are also obtained. The results proved in the paper extend and generalize several known results including those of M. Abbas and JK Kim [Bull. Korean Math. Soc. 44 (2007) 537-

On common fixed points and best approximation on nonconvex sets

Abstract: By generalizing a theorem of G. Meinardus [Arch. Rational Mech. Anal. 14 (1963), 301-30... more

Common Fixed Point of Generalized Rational Type Contraction Mappings in Partially Ordered Metric Spaces

Some common fixed point results for generalized weak contractive condition satisfying rational ty... more

Some common fixed point theorems for Ciric type contraction mappings

Abstract Some common fixed point theorems for\'{C} iri\'{c} type contraction mappings have been o... more Abstract Some common fixed point theorems for\'{C} iri\'{c} type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these type of mappings are obtained. The proved results generalize, unify and extend some of the results of the literature.

A fixed point result for weakly Kannan type cyclic contractions

In this article, we introduce the notion of Kannan type cyclic weakly contraction and derive the ... more

Fixed Point Theory and Applications

In this article, we introduce the notion of a Chatterjea-type cyclic weakly contraction and deriv... more In this article, we introduce the notion of a Chatterjea-type cyclic weakly contraction and derive the existence of a fixed point for such mappings in the setup of complete metric spaces. Our result extends and improves some fixed point theorems in the literature. Example is given to support the usability of the result.

COMMON FIXED POINTS AND INVARIANT APPROXIMATION FOR BANACH OPERATOR PAIRS WITH CIRIC TYPE NONEXPANSIVE MAPPINGS

Abstract Some common fixed point theorems for Banach operator pairs with Ciric type nonexpansive ... more Abstract Some common fixed point theorems for Banach operator pairs with Ciric type nonexpansive mappings, and the existence of common fixed points of best approximation have been proved in the framework of convex metric spaces. The results proved in the paper generalize and extend some of the results of N. Hussain (Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions, J. Math. Anal. Appl.

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Sufficient conditions for the existence of a common fixed point of generalized-weakly contractive... more Sufficient conditions for the existence of a common fixed point of generalized-weakly contractive noncommuting mappings are derived. As applications, some results on the set of best approximation for this class of mappings are obtained. The proved results generalize and extend various known results in the literature.

Some Coupled Common Fixed Point Theorems for a Pair of Mappings Satisfying a Contractive Condition of Rational Type without Monotonicity

Abstract. The purpose of this paper is to establish some coupled coincidence point theorems for a... more Abstract. The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings without mixed monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.

Fixed Points, Common Fixed Points and Invariant Approximation

Abstract Some new fixed point and common fixed point theorems for nonexpansive and generalized no... more Abstract Some new fixed point and common fixed point theorems for nonexpansive and generalized nonexpansive mapppings have been proved in the framework of metric spaces. Invaraint approximation results have been obtained for these types of mappings as applications. Our results generalize and extend several known results available in the literature.

SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS

Narang, TD, and Chandok, Sumit. &amp;amp;amp;quot;Some fixed point theorems with applications... more Narang, TD, and Chandok, Sumit. &amp;amp;amp;quot;Some fixed point theorems with applications to best simultaneous approximations..&amp;amp;amp;quot; The Journal of Nonlinear Sciences and its Applications 3.2 (2010): 87-95. &amp;amp;amp;lt;http://eudml.org/doc/226022&amp;amp;amp;gt;. ... You must be logged in to post comments. ... You must be logged in to use personal lists. ... To add item to personal list choose desired list from select box or create new one. ... To close, click the Close button or hit the ESC key. ... This article was successfully added to collection. ... To close, click the Close button or hit the ESC key.

Invariant Points and ε-Simultaneous Approximation

International Journal of …, Jan 1, 2011

We generalize and extend Brosowski-Meinardus type results on invariant points from the set of bes... more We generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of ε-simultaneous approximation. As a consequence some results on ε-approximation and best approximation are also deduced. The results proved in this paper generalize and extend some of the known results on the subject.

Common fixed points and invariant approximation for Gregus type contraction mappings

Rendiconti del Circolo Matematico di Palermo, Jan 1, 2011

Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex ... more 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.

ε-simultaneous approximation and invariant points

Bulletin of the Belgian Mathematical …, Jan 1, 2011

Abstract In this paper we generalize and extend Brosowski-Meinardus type results on invariant poi... more Abstract In this paper we generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of ε-simultaneous approximation. As a consequence some results on ε-approximation and best approximation are also deduced. The results proved extend and generalize some of the results of RN Mukherjee and V. Verma [Bull. Cal. Math. Soc. 81 (1989) 191-196; Publ. de l&amp;amp;amp;#x27;Inst. Math. 49 (1991) 111-116], TD Narang and S. Chandok [Mat. Vesnik 61 (2009) 165-171; Selçuk J. ...

Some common fixed point theorems for generalized f-weakly contractive mappings

Some approximate fixed point results and application on graph theory for partial (h-F)-generalized convex contraction mappings with special class of functions on complete metric space

In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgenerali... more In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgeneralized) convex contractions of order 3 (and with rank 3) using some auxiliary functions. Also we present some approximate fixed point results in metric space and approximate fixed point results in metric space endowed with a graph. Some examples are provided to illustrate the main results and to show the essentiality of the given hypotheses.

Generalized Krasnoselskii fixed point theorem involving auxiliary functions in bimetric spaces and application to two-point boundary value problem

In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary funct... more In this paper, we introduce a generalized contraction of Krasnoselskii-type using auxiliary functions, and obtained some sufficient conditions for existence and uniqueness of fixed point for such mappings on bimetric spaces. We also establish a result on coincidence point of two mappings, and derive several corollaries of our main theorems. As application, we establish an existence result for a two-point boundary value problem of second order differential equation.

Common fixed points and invariant approximation of R -subweakly commuting maps in convex metric spaces

Ukrainian Mathematical Journal, 2011

Sufficient conditions for the existence of a common fixed point of R-subweakly commuting mappings... more Sufficient conditions for the existence of a common fixed point of R-subweakly commuting mappings are established within the framework of a convex metric space. As applications, we obtain various results on the best approximation for this class of mappings generalizing the results known from the literature.

Some common fixed point theorems for generalized nonlinear contractive mappings

Computers & Mathematics With Applications, 2011

In this paper, we first prove a common fixed point theorem for generalized nonlinear contraction ... more

Some Common Fixed Point Results for generalized weak contractive Mappings in Partially Ordered Metric Spaces

Page 1. SOME COMMON FIXED POINT RESULTS FOR GENERALIZED WEAK CONTRACTIVE MAPPINGS IN PARTIALLY OR... more

Common Fixed Points and Invariant Approximations for Cq-commuting Generalized Nonexpansive Mappings

Abstract. Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings hav... more Abstract. Some common fixed point theorems for Cq-commuting generalized nonexpansive mappings have been proved in metric spaces. As applications, invariant approximation results are also obtained. The results proved in the paper extend and generalize several known results including those of M. Abbas and JK Kim [Bull. Korean Math. Soc. 44 (2007) 537-

On common fixed points and best approximation on nonconvex sets

Abstract: By generalizing a theorem of G. Meinardus [Arch. Rational Mech. Anal. 14 (1963), 301-30... more

Common Fixed Point of Generalized Rational Type Contraction Mappings in Partially Ordered Metric Spaces

Some common fixed point results for generalized weak contractive condition satisfying rational ty... more

Some common fixed point theorems for Ciric type contraction mappings

Abstract Some common fixed point theorems for\'{C} iri\'{c} type contraction mappings have been o... more Abstract Some common fixed point theorems for\'{C} iri\'{c} type contraction mappings have been obtained in convex metric spaces. As applications, invariant approximation results for these type of mappings are obtained. The proved results generalize, unify and extend some of the results of the literature.

A fixed point result for weakly Kannan type cyclic contractions

In this article, we introduce the notion of Kannan type cyclic weakly contraction and derive the ... more

Fixed Point Theory and Applications

In this article, we introduce the notion of a Chatterjea-type cyclic weakly contraction and deriv... more In this article, we introduce the notion of a Chatterjea-type cyclic weakly contraction and derive the existence of a fixed point for such mappings in the setup of complete metric spaces. Our result extends and improves some fixed point theorems in the literature. Example is given to support the usability of the result.

COMMON FIXED POINTS AND INVARIANT APPROXIMATION FOR BANACH OPERATOR PAIRS WITH CIRIC TYPE NONEXPANSIVE MAPPINGS

Abstract Some common fixed point theorems for Banach operator pairs with Ciric type nonexpansive ... more Abstract Some common fixed point theorems for Banach operator pairs with Ciric type nonexpansive mappings, and the existence of common fixed points of best approximation have been proved in the framework of convex metric spaces. The results proved in the paper generalize and extend some of the results of N. Hussain (Common fixed points in best approximation for Banach operator pairs with Ciric type I-contractions, J. Math. Anal. Appl.

Common Fixed Points, Invariant Approximation and Generalized Weak Contractions

Sufficient conditions for the existence of a common fixed point of generalized-weakly contractive... more Sufficient conditions for the existence of a common fixed point of generalized-weakly contractive noncommuting mappings are derived. As applications, some results on the set of best approximation for this class of mappings are obtained. The proved results generalize and extend various known results in the literature.

Some Coupled Common Fixed Point Theorems for a Pair of Mappings Satisfying a Contractive Condition of Rational Type without Monotonicity

Abstract. The purpose of this paper is to establish some coupled coincidence point theorems for a... more Abstract. The purpose of this paper is to establish some coupled coincidence point theorems for a pair of mappings without mixed monotone property satisfying a contractive condition of rational type in the framework of partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.

Fixed Points, Common Fixed Points and Invariant Approximation

Abstract Some new fixed point and common fixed point theorems for nonexpansive and generalized no... more Abstract Some new fixed point and common fixed point theorems for nonexpansive and generalized nonexpansive mapppings have been proved in the framework of metric spaces. Invaraint approximation results have been obtained for these types of mappings as applications. Our results generalize and extend several known results available in the literature.

SOME FIXED POINT THEOREMS WITH APPLICATIONS TO BEST SIMULTANEOUS APPROXIMATIONS

Narang, TD, and Chandok, Sumit. &amp;amp;amp;quot;Some fixed point theorems with applications... more Narang, TD, and Chandok, Sumit. &amp;amp;amp;quot;Some fixed point theorems with applications to best simultaneous approximations..&amp;amp;amp;quot; The Journal of Nonlinear Sciences and its Applications 3.2 (2010): 87-95. &amp;amp;amp;lt;http://eudml.org/doc/226022&amp;amp;amp;gt;. ... You must be logged in to post comments. ... You must be logged in to use personal lists. ... To add item to personal list choose desired list from select box or create new one. ... To close, click the Close button or hit the ESC key. ... This article was successfully added to collection. ... To close, click the Close button or hit the ESC key.

Invariant Points and ε-Simultaneous Approximation

International Journal of …, Jan 1, 2011

We generalize and extend Brosowski-Meinardus type results on invariant points from the set of bes... more We generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of ε-simultaneous approximation. As a consequence some results on ε-approximation and best approximation are also deduced. The results proved in this paper generalize and extend some of the known results on the subject.

Common fixed points and invariant approximation for Gregus type contraction mappings

Rendiconti del Circolo Matematico di Palermo, Jan 1, 2011

Existence of common fixed points for generalized S-nonexpansive subcompatible mappings in convex ... more 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.

ε-simultaneous approximation and invariant points

Bulletin of the Belgian Mathematical …, Jan 1, 2011

Abstract In this paper we generalize and extend Brosowski-Meinardus type results on invariant poi... more Abstract In this paper we generalize and extend Brosowski-Meinardus type results on invariant points from the set of best approximation to the set of ε-simultaneous approximation. As a consequence some results on ε-approximation and best approximation are also deduced. The results proved extend and generalize some of the results of RN Mukherjee and V. Verma [Bull. Cal. Math. Soc. 81 (1989) 191-196; Publ. de l&amp;amp;amp;#x27;Inst. Math. 49 (1991) 111-116], TD Narang and S. Chandok [Mat. Vesnik 61 (2009) 165-171; Selçuk J. ...

Some common fixed point theorems for generalized f-weakly contractive mappings