Class Of Self-mappings Research Articles

Fixed point existence results of F-Kannan type contraction on a metric space with directed graph

In this article, we have attained some interesting results on existence of fixed points for a newly developed larger class of self mappings called FG -Kannan defined on a metric space equipped with a special type of graph called ʊ-orbitally connected graph. This extended class is a merger of the most recently developed Kannan type mapping called F-Kannan contractions defined in a metric space and G-Kannan mapping defined in a metric space with an underlying graph. It is highlighted through example that such a graph condition is sufficient to study fixed points of FG -Kannan mappings. Several interesting examples are illustrated which justify that our obtained results are more general and further, many previously developed fixed point results related to Kannan mappings are encompassed in our main result. The article closes by raising some open problems of this work.

Fixed point existence results of F-Kannan type contraction on a metric space with directed graph

In this article, we have attained some interesting results on existence of fixed points for a newly developed larger class of self mappings called FG -Kannan defined on a metric space equipped with a special type of graph called ʊ-orbitally connected graph. This extended class is a merger of the most recently developed Kannan type mapping called F-Kannan contractions defined in a metric space and G-Kannan mapping defined in a metric space with an underlying graph. It is highlighted through example that such a graph condition is sufficient to study fixed points of FG -Kannan mappings. Several interesting examples are illustrated which justify that our obtained results are more general and further, many previously developed fixed point results related to Kannan mappings are encompassed in our main result. The article closes by raising some open problems of this work.

Coincidence and Fixed Point of Nonexpansive Type Mappings in 2-Metric Spaces

The aim of this paper is to prove a coincidence point theorem for a class of self mappings satisfying nonexpansive type condition under various conditions and a fixed point theorem is also obtained. Our results extend and generalize the corresponding result of Singh and Chandrashekhar [A fixed point theorem in a 2-metric space and an application, J. Natural and Physical Sci. 15(1-2) (2001), 55-64].

On Ω Class of Mappings in a p-Cyclic Complete Metric Space

In this manuscript, we introduce the concept of Ω -class of self mappings on a metric space and a notion of p-cyclic complete metric space for a natural number ( p ≥ 2 ) . We not only give sufficient conditions for the existence of best proximity points for the Ω -class self-mappings that are defined on p-cyclic complete metric space, but also discuss the convergence of best proximity points for those mappings.

Fixed Point Theorems in Fuzzy Metric Spaces

I n the present work, we establish several fixed point theorems for a new class of self-maps in M-complete fuzzy metric spaces and compact fuzzy metric spaces, respectively.

Existence of common fixed point and best proximity point for generalized nonexpansive type maps in convex metric space.

Here, we extend the notion of (E.A.) property in a convex metric space defined by Kumar and Rathee (Fixed Point Theory Appl 1–14, 2014) by introducing a new class of self-maps which satisfies the common property (E.A.) in the context of convex metric space and ensure the existence of common fixed point for this newly introduced class of self-maps. Also, we guarantee the existence of common best proximity points for this class of maps satisfying generalized non-expansive type condition. We furnish an example in support of the proved results.

Common Fixed Point Theorems in Fuzzy Metric Spaces

We establish a common xed point theorem for a new class of self-maps in M- complete fuzzy metric spaces and we give some ap- plications for mappings satisfying contractive inequalities of integral type. We support our results by examples.

Some common fixed point and invariant approximation results for nonexpansive mappings in convex metric space

In this work, we introduce a new class of self-maps which satisfy the (E.A.) property with respect to some , where M is q-starshaped subset of a convex metric space and common fixed point results are established for this new class of self-maps. After that we obtain some invariant approximation results as an application. Our results represent a very strong variant of the several recent results existing in the literature. We also provide some illustrative examples in the support of proved results. MSC:46T99, 47H10, 54H25.

Common Fixed Point For Affine Self Maps Invariant Approximation In P-normed Spaces

Common fixed point results for new classes of non-commuting self-maps and non-expansive. Within the class of all self-maps \(f\) and \(T\) of a \(W\)−starshaped subset \(M\) of \(X\) where \(f\) is affine or \(W\)−affine. We apply them to obtain several invariant approximation results which unify, extend, and complement well-known results.

Minimization of the number of periodic points for smooth self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers

Abstract Let f be a smooth self-map of m-dimensional, m ≥ 4, smooth closed connected and simply-connected manifold, r a fixed natural number. For the class of maps with periodic sequence of Lefschetz numbers of iterations the authors introduced in [Graff G., Kaczkowska A., Reducing the number of periodic points in smooth homotopy class of self-maps of simply-connected manifolds with periodic sequence of Lefschetz numbers, Ann. Polon. Math. (in press)] the topological invariant J[f] which is equal to the minimal number of periodic points with the periods less or equal to r in the smooth homotopy class of f. In this paper the invariant J[f] is computed for self-maps of 4-manifold M with dimH 2(M; ℚ) ≤ 4 and estimated for other types of manifolds. We also use J[f] to compare minimization of the number of periodic points in smooth and in continuous categories.

Fixed point theorems in fuzzy metric spaces

In the present work, we establish several fixed point theorems for a new class of self-maps in M -complete fuzzy metric spaces and compact fuzzy metric spaces, respectively.

On a conjecture of Ōshima

The set of homotopy classes of self maps of a compact, connected Lie group G is a group by the pointwise multiplication which we denote by H ( G ) , and it is known to be nilpotent. Ōshima [H. Ōshima, Self homotopy group of the exceptional Lie group G 2 , J. Math. Kyoto Univ. 40 (1) (2000) 177–184] conjectured: if G is simple, then H ( G ) is nilpotent of class ⩾ rank G . We show this is true for PU ( p ) which is the first high rank example.

Fixed Point Theorems in Cone Banach Spaces

AbstractIn this manuscript, a class of self-mappings on cone Banach spaces which have at least one fixed point is considered. More precisely, for a closed and convex subset "Equation missing" of a cone Banach space with the norm "Equation missing", if there exist "Equation missing", "Equation missing", "Equation missing" and "Equation missing" satisfies the conditions "Equation missing" and "Equation missing" for all "Equation missing" , then "Equation missing" has at least one Fixed point.

Coincidence and fixed points of non-expansive type mappings on 2-metric spaces

In this paper a unique coincidence value is obtained for a class of self mappings satisfying non-expansive type condition on 2-metric spaces under various conditions and a fixed point theorem is also obtained.

Inertial Iterative Process for Fixed Points of Certain Quasi-nonexpansive Mappings

This paper deals with a general formalism which consists in approximating a point in a nonempty set \(S\), in a real Hilbert space \(H\), by a sequence \((x_n) \subset H\) such that \(x_{{n + 1}} : = {\user1{\mathcal{T}}}_{n} {\left( {x_{n} + \theta _{n} {\left( {x_{n} - x_{{n - 1}} } \right)}} \right)}\), where \({\left( {\theta _{n} } \right)} \subset \left[ {0,} \right.\left. 1 \right)\), \(x_0\)\(x_1\) are in \(H\) and \({\left( {{\user1{\mathcal{T}}}_{n} } \right)}_{{n \geqslant 0}}\) is a sequence included in a certain class of self-mappings on \(H\), such that every fixed point set of \({\user1{\mathcal{T}}}_{n}\) contains \(S\). This iteration method is inspired by an implicit discretization of the second order ‘heavy ball with friction’ dynamical system. Under suitable conditions on the parameters and the operators \({\left( {{\user1{\mathcal{T}}}_{n} } \right)}\), we prove that this scheme generates a sequence which converges weakly to an element of \(S\). In particular, by appropriate choices of \({\left( {{\user1{\mathcal{T}}}_{n} } \right)}\), this algorithm works for approximating common fixed points of infinite countable families of a wide class of operators which includes \(\alpha\)-averaged quasi-nonexpansive mappings for \(\alpha \in {\left( {0,\;1} \right)}\).

$\boldsymbol {\pi _*}$-kernels of Lie groups

We study a filtration on the group of homotopy classes of self maps of a compact Lie group associated with homotopy groups. We determine these filtrations of $SU(3)$ and $Sp(2)$ completely. We introduce two natural invariants $lz_p(X)$ and $sz_p(X)$ defined by the filtration, where $p$ is a prime number, and compute the invariants for simple Lie groups in the cases where Lie groups are $p$-regular or quasi $p$-regular. We apply our results to the groups of self homotopy equivalences.

A new class of nonexpansive type mappings and fixed points

In this paper a new class of self-mappings on metric spaces, which satisfy the nonexpensive type condition (3) below is introduced and investigated. The main result is that such mappings have a unique fixed point. Also, a remetrization theorem, which is converse to Banach contraction principle is given.

Periodic and fixed point theorems in a quasi-metric space

AbstractGeneral periodic and fixed point theorems are proved for a class of self maps of a quasi-metric space which satisfy the contractive definition (A) below. Two examples are presented to show that the class of mappings which satisfy (A) is indeed wider than a class of selfmaps which satisfy Caristi's contractive definition (C) below. Also a common fixed point theorem for a pair of maps which satisfy a contractive condition (D) below is established.