generalized contraction

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Generalized contraction mapping principle and generalized best proximity point theorems in probabilistic metric spaces

Generalized contraction mapping principle and generalized best proximity point theorems in probabilistic metric spaces

The purpose of this paper is to introduce some basic definitions about fixed point and best proximity point in two classes of probabilistic metric spaces and to prove contrac- tion mapping principle and relevant best proximity point theorems. The first class is the so-called S-probabilistic metric spaces. In S-probabilistic metric spaces, the generalized contraction mapping principle and generalized best proximity point theorems have been proved by authors. These results improve and extend the recent results of Su and Zhang []. The second class is the so-called Menger probabilistic metric spaces. In Menger prob- abilistic metric spaces, the contraction mapping principle and relevant best proximity point theorems have been proved by authors. These results also improve and extend the results of many authors. In order to get the results of this paper, some new methods have been used. Meanwhile some error estimate inequalities have been established.
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Modified noor iterations for nonexpansive semigroups with generalized contraction in Banach spaces

Modified noor iterations for nonexpansive semigroups with generalized contraction in Banach spaces

equivalence between Moudafi’s viscosity approximation with contractions and Brow- der-type iterative processes (Halpern-type iterative processes); see [14] for more details. In this article, inspired by above result, we introduce and study the explicit viscosity iterative scheme for the generalized contraction f and a nonexpansive semigroup {T(t) : t ≥ 0}:

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Generalized contraction principle

Generalized contraction principle

Fixed point theorems are proved for contraction maps on M-convex spaces... Fixed Point Theorems, Contraion principle, M-convex spaces..[r]

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Common fixed point results for generalized contraction  mappings in b - metric space

Common fixed point results for generalized contraction mappings in b - metric space

Fixed point theory is rapidly moving into the mainstream of Mathematics mainly because of its applications in diverse fields which include numerical methods like Newton-Raphson method, establishing Picard’s existence theorem, existence of solution of integral equations and a system of linear equations. In 1922, S. Banach [1], The first important and significant result was proved a fixed point theorem for contraction mappings in complete metric space and also called it Banach fixed point theorem / Banach contraction principle which is considered as the mile stone in fixed point theory. This theorem states that, A mapping : → where( , ) is a metric space, is said to be a contraction if there exists ∈ [0,1) such that
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Generalized Contraction Mapping and Fixed Point Theorems in Complete Metric Space

Generalized Contraction Mapping and Fixed Point Theorems in Complete Metric Space

Poincare [17] was the first to work in this field Fixed Point Theory. Then Brouwer [4] in 1912, proved fixed point theorem for the solution of the equation ( ) = . He also proved fixed point theorem for a square, a sphere and their n-dimensional parts which means further extended by Kakutani [15] in 1922, Banach [5] proved that a contraction mapping in complete metric space possessed a unique fixed point.

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Fixed points of generalized contraction maps in metric spaces

Fixed points of generalized contraction maps in metric spaces

generalizations of Banach contraction principle, some generalizations of contraction condition was obtained in ( [7] - [10], [13] ). Recently Hussain, Parvaneh, samet and Vetro [9] introduced a new contraction map, namely JS-contraction map and proved the existence and uniqueness of fixed points in complete metric spaces.

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Common fixed points of generalized contraction maps in metric spaces

Common fixed points of generalized contraction maps in metric spaces

direction or/and generalization of ambiant spaces of the operator under consideration on the other. Banach contraction principle [5] which states that if (X , d) is complete metric space and T : X → X is a contraction map then T has a unique fixed point, is a fundamental result in this theory. Due to its importance and simplicity several authors have obtained many interesting extensions and generalizations of Banach contraction principle, some generalizations of con- traction condition was obtained ([6]-[9], [12]). Recently, Hussain, Parvanch, Samet and Vetro [8] introduced a new contraction map, namely JS-contraction map and proved the existence and uniqueness of fixed points in complete metric spaces.
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Generalized contraction principle under relatively weaker contraction in partial metric spaces

Generalized contraction principle under relatively weaker contraction in partial metric spaces

The very first contribution to fixed point theory was due to Banach [3] in 1922. He con- ferred the celebrated result in his thesis, namely the Banach contraction principle. Later on, many researchers, fascinated by his idea, extended this result in various directions. One of these is by generalizing the metric. In this direction, Matthews [4] in 1994 pre- sented the idea of a partial metric by extending the concept of metric and proved a sup- plementary result of the Banach contraction principle in partial metric spaces. Thereafter, many results on the fixed points in partial metric spaces were established (see [5–14] and the references therein).
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Fixed point theorems with generalized altering distance functions in partially ordered metric spaces via w-distances and applications

Fixed point theorems with generalized altering distance functions in partially ordered metric spaces via w-distances and applications

Another recent direction of such generalizations, see [–], has been studied by weak- ening the contractive conditions and, in compensation, by simultaneously enriching the metric space structure with a partial order. Very recently, Su [] presented the definition of generalized altering distance function to prove the following new fixed point theorem of generalized contraction mappings in a complete metric space endowed with a partial order.

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A generalized weak contraction principle with applications to coupled coincidence point problems

A generalized weak contraction principle with applications to coupled coincidence point problems

In this paper we establish some coincidence point results for generalized weak contractions with discontinuous control functions. The theorems are proved in metric spaces with a partial order. Our theorems extend several existing results in the current literature. We also discuss several corollaries and give illustrative examples. We apply our result to obtain some coupled coincidence point results which effectively generalize a number of established results.

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Periodic points for the weak contraction mappings in complete generalized metric spaces

Periodic points for the weak contraction mappings in complete generalized metric spaces

In 2000, Branciari [5] introduced the following notion of a generalized metric space where the triangle inequality of a metric space had been replaced by an inequality involing three terms instead of two. Later, many authors worked on this interesting space (e.g. [6-11]).

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Probabilistic G-contractions

Probabilistic G-contractions

In this paper we introduce the notion of probabilistic G-contraction and establish some fixed point theorems in such settings. Our results generalize/extend some recent results of Jachymski and Sehgal and Bharucha-Reid. Consequently, we obtain fixed point results for ( , δ )-chainable PM-spaces and for cyclic operators.

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Fixed Point Results for Geraghty Type Generalized F-contraction for Weak alpha-admissible Mapping in Metric-like Spaces

Fixed Point Results for Geraghty Type Generalized F-contraction for Weak alpha-admissible Mapping in Metric-like Spaces

Abstract. In this paper, we establish the existence of some fixed point results for generalized (α, β, F )-Geraghty contraction in metric-like spaces. We provide an example in order to support our results where some consequence applications of such result will be considered in this article. The obtained results improve and extend some well-known common fixed point results in the literature.

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MATHEMATICAL MORPHOLOGY BASED CHARACTERIZATION OF BINARY IMAGE

MATHEMATICAL MORPHOLOGY BASED CHARACTERIZATION OF BINARY IMAGE

This paper is organized as follows: We define ‘dilation asymmetry’ and ‘erosion asymmetry’ in the next section. These terms are not mentioned in classical mathematical morphology and are defined in this paper to elaborate smoothing of an image by expansion and contraction respectively. After this, we generalize these terms for multiscale smoothing and show their oneness respectively with ridge and skeleton. This is followed by a discussion on shape-size complexities of image background and foreground along with their ‘degree of stability’, respectively via multiple close- hulls and open-skulls, under the influence of increasing cycles of morphological closing and opening. We also propose algorithms to obtain critical scales corresponding to multiple close-hulls and open-skulls of an image along with their degree of stability. Afterwards, we demonstrate experimental results of these algorithms on deterministic and random binary Koch quadric fractals. As an outcome of analysis of these algorithms, we define systematic quantization techniques to quantify image and its background into zonal fragments with open-skulls and close-hulls res- pectively being the quantifiers. There exist various techniques to estimate morphology based fractal dimen- sion (e.g. Maragos and Sun, 1993; Radhakrishnan et al., 2004). We compute a scale invariant but shape- dependent morphological quantitative index and correlate this with analytical fractal dimension of binary fractal. The paper ends with conclusion of the results of our study.
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φ-Contraction in generalized probabilistic metric spaces

φ-Contraction in generalized probabilistic metric spaces

In the same vein probabilistic generalized metric spaces have been introduced by Zhou et al. [] wherein they also proved certain primary fixed point results in these spaces. An interesting class of problems in probabilistic fixed point theory was addressed in re- cent times by use of gauge functions. These are control functions which have been used to extend the Sehgal contraction in probabilistic metric spaces. Some examples of these applications are in [, , , , , ]. One of such gauge functions was introduced by Fang []. Here we use the gauge function used by Fang [] to obtain a fixed point result in probabilistic G-metric spaces. Our result is supported with an example.
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Extensions of Ćirić and Wardowski type fixed point theorems in D-generalized metric spaces

Extensions of Ćirić and Wardowski type fixed point theorems in D-generalized metric spaces

The purpose of this paper is to modify the Ćirić quasi-contractions. In this paper we introduce D-admissible mappings and establish the fixed point theorem for Ćirić quasi- contractions with the help of D-admissible mappings. This article includes an example of a D-generalized metric space to show that a sequence in this setting may be convergent without being a Cauchy sequence. We also investigate the existence and uniqueness of a fixed point for the mappings satisfying nonlinear rational contraction and Wardowski type F-contraction, where the function F is taken from a more general class of functions than that known in the existing literature.
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Fixed point theorems and partial metric spaces

Fixed point theorems and partial metric spaces

In 1992, the notion of partial metric space was introduced by Matthews [7] as a part of the study of denotational semantics of dataflow networks. Henceforward, many authors made ef- forts to study various fixed point theorems and obtained a lot of perfect results. Ravi P Agarwal [10] proved some fixed point results for generalized cyclic contraction on partial metric spaces. M ˘ ad ˘ alina and Ioan [3] proved a Maia type fixed point theorem for cyclic ϕ -contraction, which extended the results of W.A. Kirk [9]. Z. Qingnian and S. Yisheng [12] proved fixed point re- sults for single-valued hybrid generalized ϕ-weak contractions. Very recently, many new fixed point results were established by Yi Zhang, Jiang Zhu [8] and L.N. Mishra [11], etc.
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Coincidence and Common Fixed Point Using Sequentially Weak Contractive Mapping

Coincidence and Common Fixed Point Using Sequentially Weak Contractive Mapping

[10]. Moradi S. and Farajzadeh A., On the fixed point of ( 𝜓 − 𝜑 ) - weak and generalized (𝜓 − 𝜑) - weak contraction mappings, Applied Mathematics Letters 25 (2012), 1257-1262. [11]. Nadler,S.B.JR. sequence of contractions and

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The existence and convergence of best proximity points for generalized proximal contraction mappings

The existence and convergence of best proximity points for generalized proximal contraction mappings

Let X be an arbitrary nonempty set. A fixed point for a self-mapping T : X → X is a point x ∈ X such that Tx = x. The applications of fixed point theory are very important in diverse disciplines of mathematics, statistics, chemistry, biology, computer science, engineering, and economics. One of the very popular tools of fixed point theory is the Banach con- traction principle, which first appeared in . It states that if (X, d) is a complete metric space and T : X → X is a contraction mapping (i.e., d(Tx, Ty) ≤ αd(x, y) for all x, y ∈ X, where α ∈ [, )), then T has a unique fixed point. It has been generalized in different ways by mathematicians over the years (see [–]). However, almost all such results relate to the existence of a fixed point for self-mappings.
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A Common End Point Theorem for Set-Valued Generalized -Weak Contraction

A Common End Point Theorem for Set-Valued Generalized -Weak Contraction

We introduce the class of generalized ψ, ϕ-weak contractive set-valued mappings on a metric space. We establish that such mappings have a unique common end point under certain weak conditions. The theorem obtained generalizes several recent results on single-valued as well as certain set-valued mappings.

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