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S.N. Mishra

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Allama Iqbal Open University

Dr. Sudipta K. Ghosh

Wutiphol Sintunavarat

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Papers by S.N. Mishra

Common Fixed Point Theorems for --Contractive Type Mappings

International Journal of Analysis, 2013

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive type mappings. They establi... more Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive type mappings. They established some fixed point theorems for these mappings in complete metric spaces. In this paper, we introduce the notion of a coupledα-ψ-contractive mapping and give a common fixed point result about the mapping. Also, we give a result of common fixed points of some coupled self-maps on complete metric spaces satisfying a contractive condition.

On asymptotically nonexpansive mappings in q-hyperconvex T0-quasi-metric spaces

In this note a well known result of Khamsi [Proc. Amer. Math. Soc. 132 (2004), 365-373] onapproxi... more

A Note on the Weak Convergence of a Sequence of Successive Approximations

Demonstratio Mathematica, 2006

In this paper we discuss the weak convergence of the sequence of successive approximations for a ... more

Erratum to “Suzuki contraction theorem on a 2-metric space”

Recently T. Suzuki [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)] obtained a... more Recently T. Suzuki [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)] obtained a forceful generalization of the classical Banach contraction theorem in metric spaces. In this paper, we obtain an analogue of the same in 2-metric spaces. As an application, we obtain a coincidence theorem for a pair of maps on an arbitrary set with values in a 2-metric space.

Some Existence and Convergence Theorems for Nonexpansive Type Mappings

International Journal of Analysis, 2013

Some existence and convergence theorems for a class of nonexpansive type mappings are obtained in... more

On finitistic spaces

Topology and its Applications, 1999

Finitistic spaces form a natural class containing compact and finite-dimensional spaces. Introduc... more Finitistic spaces form a natural class containing compact and finite-dimensional spaces. Introduced and investigated by fixed-point theorists, finitistic spaces found an application in cohomological dimension theory. In the paper, two characterizations of paracompact, finitistic spaces are proved. These characterizations allow to create a mechanism of generalizing results of finite dimension theory. As an application we obtain results on compact group actions on paracompact spaces which were previously known for compact Lie group actions.

Fixed point theorems in uniform spaces

Results in Mathematics, 1983

Fixed point theorems in a Hausdorff uniform space are proved by considering a contractive type co... more

Fixed and best proximity points for cyclic weakly contraction mappings

In this paper we obtain some fixed and best proximity point theorems for cyclic (ψ, ϕ)-weakly con... more

Fixed points of cyclic weak contractions in metric spaces

In this paper the well known notion of a cyclic contraction for a finite family of non-empty subs... more In this paper the well known notion of a cyclic contraction for a finite family of non-empty subsets of a metric space X and a mapping T of X into X (respectively, into the collection of nonempty subsets of X) has been generalized. Subsequently, the above idea is used to obtain some new fixed point theorems for single and multi-valued mappings. The results obtained herein generalize some recent fixed point theorems.

Fixed Point Theorems in a Locally Convex Space

Quaestiones Mathematicae, 1996

ABSTRACT

Fixed point theorems for single-valued and multi-valued maps

Nonlinear Analysis: Theory, Methods & Applications, 2011

Let X be a non-empty set and T be a self map on X. A point x 0 ∈ X is called a fixed point of T i... more Let X be a non-empty set and T be a self map on X. A point x 0 ∈ X is called a fixed point of T if Tx 0 = x 0 ; that is, a point which remains invariant under the transformation T is called a fixed point of T. () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 4 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 4 / 49 Chapter 2 Common fixed point theorems for multi-valued and single-valued maps in complete metric space () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 5 / 49 xed point theorems for multi-valued and single-valued maps Let (X , d) be a metric space. Denote by CB(X) the collection of non-empty closed bounded subsets of X. For A, B ∈ CB(X) and x ∈ X , define D(x, A) = inf a∈A d(x, a) and H(A, B) = max sup a∈A D(a, B), sup b∈B D(b, A) () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 6 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 8 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 9 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 36 / 49

On general hybrid contractions

Journal of the Australian Mathematical Society, 1999

Khan et al. have studied the existence of solutions of functional equations f,x e Sx f) Tx and x ... more Khan et al. have studied the existence of solutions of functional equations f,x e Sx f) Tx and x = F,x e Sx n Tx under certain nonlinear hybrid contraction and asymptotic regularity conditions, generalizing many known results on coincidences and fixed points. However, most of their main theorems admit counter examples. In this paper, we rectify these results and obtain many coincidence and fixed point theorems in a more general setting.

Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

International Journal of Mathematics and Mathematical Sciences, 2002

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and... more It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

$Research paper thumbnail of A new approach to superfractals$

A new approach to superfractals

Chaos, Solitons & Fractals, 2009

V-variable fractals and superfractals have recently been introduced by Barnsley [Barnsley Michael... more

Stability of Jungck-type iterative procedures

International Journal of Mathematics and Mathematical Sciences, 2005

We introduce and discuss the stability of Jungck and Jungck-Mann iterative procedures for a pair ... more

Common Fixed Point Theorems for --Contractive Type Mappings

International Journal of Analysis, 2013

Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive type mappings. They establi... more Recently, Samet et al. (2012) introduced the notion ofα-ψ-contractive type mappings. They established some fixed point theorems for these mappings in complete metric spaces. In this paper, we introduce the notion of a coupledα-ψ-contractive mapping and give a common fixed point result about the mapping. Also, we give a result of common fixed points of some coupled self-maps on complete metric spaces satisfying a contractive condition.

On asymptotically nonexpansive mappings in q-hyperconvex T0-quasi-metric spaces

In this note a well known result of Khamsi [Proc. Amer. Math. Soc. 132 (2004), 365-373] onapproxi... more

A Note on the Weak Convergence of a Sequence of Successive Approximations

Demonstratio Mathematica, 2006

In this paper we discuss the weak convergence of the sequence of successive approximations for a ... more

Erratum to “Suzuki contraction theorem on a 2-metric space”

Recently T. Suzuki [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)] obtained a... more Recently T. Suzuki [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)] obtained a forceful generalization of the classical Banach contraction theorem in metric spaces. In this paper, we obtain an analogue of the same in 2-metric spaces. As an application, we obtain a coincidence theorem for a pair of maps on an arbitrary set with values in a 2-metric space.

Some Existence and Convergence Theorems for Nonexpansive Type Mappings

International Journal of Analysis, 2013

Some existence and convergence theorems for a class of nonexpansive type mappings are obtained in... more

On finitistic spaces

Topology and its Applications, 1999

Finitistic spaces form a natural class containing compact and finite-dimensional spaces. Introduc... more Finitistic spaces form a natural class containing compact and finite-dimensional spaces. Introduced and investigated by fixed-point theorists, finitistic spaces found an application in cohomological dimension theory. In the paper, two characterizations of paracompact, finitistic spaces are proved. These characterizations allow to create a mechanism of generalizing results of finite dimension theory. As an application we obtain results on compact group actions on paracompact spaces which were previously known for compact Lie group actions.

Fixed point theorems in uniform spaces

Results in Mathematics, 1983

Fixed point theorems in a Hausdorff uniform space are proved by considering a contractive type co... more

Fixed and best proximity points for cyclic weakly contraction mappings

In this paper we obtain some fixed and best proximity point theorems for cyclic (ψ, ϕ)-weakly con... more

Fixed points of cyclic weak contractions in metric spaces

In this paper the well known notion of a cyclic contraction for a finite family of non-empty subs... more In this paper the well known notion of a cyclic contraction for a finite family of non-empty subsets of a metric space X and a mapping T of X into X (respectively, into the collection of nonempty subsets of X) has been generalized. Subsequently, the above idea is used to obtain some new fixed point theorems for single and multi-valued mappings. The results obtained herein generalize some recent fixed point theorems.

Fixed Point Theorems in a Locally Convex Space

Quaestiones Mathematicae, 1996

ABSTRACT

Fixed point theorems for single-valued and multi-valued maps

Nonlinear Analysis: Theory, Methods & Applications, 2011

Let X be a non-empty set and T be a self map on X. A point x 0 ∈ X is called a fixed point of T i... more Let X be a non-empty set and T be a self map on X. A point x 0 ∈ X is called a fixed point of T if Tx 0 = x 0 ; that is, a point which remains invariant under the transformation T is called a fixed point of T. () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 4 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 4 / 49 Chapter 2 Common fixed point theorems for multi-valued and single-valued maps in complete metric space () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 5 / 49 xed point theorems for multi-valued and single-valued maps Let (X , d) be a metric space. Denote by CB(X) the collection of non-empty closed bounded subsets of X. For A, B ∈ CB(X) and x ∈ X , define D(x, A) = inf a∈A d(x, a) and H(A, B) = max sup a∈A D(a, B), sup b∈B D(b, A) () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 6 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 8 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 9 / 49 () Common Fixed Point Theorems for Single-valued and Multi-valued Maps • • 24 th ,January 2017 36 / 49

On general hybrid contractions

Journal of the Australian Mathematical Society, 1999

Khan et al. have studied the existence of solutions of functional equations f,x e Sx f) Tx and x ... more Khan et al. have studied the existence of solutions of functional equations f,x e Sx f) Tx and x = F,x e Sx n Tx under certain nonlinear hybrid contraction and asymptotic regularity conditions, generalizing many known results on coincidences and fixed points. However, most of their main theorems admit counter examples. In this paper, we rectify these results and obtain many coincidence and fixed point theorems in a more general setting.

Coincidences and fixed points of reciprocally continuous and compatible hybrid maps

International Journal of Mathematics and Mathematical Sciences, 2002

It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and... more It is proved that a pair of reciprocally continuous and nonvacuously compatible single-valued and multivalued maps on a metric space possesses a coincidence. Besides addressing two historical problems in fixed point theory, this result is applied to obtain new general coincidence and fixed point theorems for single-valued and multivalued maps on metric spaces under tight minimal conditions.

$Research paper thumbnail of A new approach to superfractals$

A new approach to superfractals

Chaos, Solitons & Fractals, 2009

V-variable fractals and superfractals have recently been introduced by Barnsley [Barnsley Michael... more

Stability of Jungck-type iterative procedures

International Journal of Mathematics and Mathematical Sciences, 2005

We introduce and discuss the stability of Jungck and Jungck-Mann iterative procedures for a pair ... more