Some coincidence and periodic points results in a metric space endowed with a graph and applications

Gopal, Dhananjay; Vetro, Calogero; Abbas, Mujahid; Patel, Deepesh Kumar

doi:10.15352/bjma/09-3-9

Cited by 16 publications

(9 citation statements)

References 13 publications

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“…First, Jachymski [16] provided fixed point results when considering graphic contractions. For other details, see [12,[17][18][19][20][21][22][23].…”

Section: Some Results For Graphic Contractionsmentioning

confidence: 99%

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New Fixed Point Results for Modified Contractions and Applications

et al. 2019

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In this study, we introduce a new type of contractive mapping to establish the existence and uniqueness of fixed points for this type of contraction. Some related examples are built demonstrating the superiority of our results compared to the existing onesin the literature. As applications of the results obtained, some new fixed point theorems are presented for graph-type contractions. Furthermore, sufficient conditions are discussed to ensure the existence underlying various approaches of a solution for a functional equation originating in dynamic programming.

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“…First, Jachymski [16] provided fixed point results when considering graphic contractions. For other details, see [12,[17][18][19][20][21][22][23].…”

Section: Some Results For Graphic Contractionsmentioning

confidence: 99%

“…Following Example 2.8 in[21], consider M = [0, 1] is endowed with the usual metric. Let G be a graph with V(G) = M and E(G)…”

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confidence: 99%

New Fixed Point Results for Modified Contractions and Applications

et al. 2019

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“…Now, following the idea in ( [15], see also [5]) , we discuss an application of fixed point techniques to the solution of the nonlinear integral equation:…”

Section: On the Existence Of Solutions For A Class Of Nonlinear Integmentioning

confidence: 99%

Generalized contraction mappings of rational type and applications to nonlinear integral equations

Morales¹,

Rojas

Bisht

2018

bspm

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The aim of the present paper is to introduce a new class of pair of contraction mappings, called ψ − (α, β, m)-contraction pairs, and obtain common fixed point theorems for a pair of mappings in this class, satisfying a minimal commutativity condition. Afterwards, we will use mappings in this class to analyze the existence of solutions for a class of nonlinear integral equations on the space of con- tinuous functions and in some of its subspaces. Concrete examples are also provided in order to illustrate the applicability of the results.

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“…This principle has been generalized and extended by many researchers, either by changing the contraction condition or the underlying space. For more details, see [2][3][4][5][6][7][8][9][10][11]. The theory of fixed points in ordered sets was started first by Turinici [12].…”

Section: Introductionmentioning

confidence: 99%