scholarly journals Ample Spectrum Contractions and Related Fixed Point Theorems

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1033 ◽  
Author(s):  
Antonio Francisco Roldán López de Roldán López de Hierro ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Point Of View ◽  
Strict Inequality ◽  
Simple Condition ◽  
Auxiliary Functions ◽  
Simulation Functions ◽  
Contractive Maps ◽  
R Functions

Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R-functions, ( R , S ) -contractions and ( A , S ) -contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.

scholarly journals Fixed Point Results forG-α-Contractive Maps with Application to Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Nawab Hussain ◽  
Vahid Parvaneh ◽  
Jamal Rezaei Roshan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Periodic Boundary ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Existence Of A Solution ◽  
First Order ◽  
Contractive Mappings ◽  
Ordered Space ◽  
Contractive Maps

We unify the concepts ofG-metric, metric-like, andb-metric to define new notion of generalizedb-metric-like space and discuss its topological and structural properties. In addition, certain fixed point theorems for two classes ofG-α-admissible contractive mappings in such spaces are obtained and some new fixed point results are derived in corresponding partially ordered space. Moreover, some examples and an application to the existence of a solution for the first-order periodic boundary value problem are provided here to illustrate the usability of the obtained results.

scholarly journals Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 143
Author(s):  
Chayut Kongban ◽  
Poom Kumam ◽  
Juan Martínez-Moreno ◽  
Kanokwan Sitthithakerngkiet
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Differential Equations ◽  
Stochastic Differential Equation ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Random Fixed Point ◽  
Contractive Mappings ◽  
Random Differential Equations ◽  
Contractive Maps

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results.

Fixed points of contractive maps on dcpo's

2013 ◽  
Vol 24 (1) ◽  
Author(s):  
E. COLEBUNDERS ◽  
S. DE WACHTER ◽  
R. LOWEN
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Scott Topology ◽  
Study Approach ◽  
Special Cases ◽  
Monotone Maps ◽  
Contractive Maps ◽  
Approach Spaces

In this paper we study approach structures on dcpo's. A dcpo (X, ≤) will be endowed with several other structures: the Scott topology; an approach structure generated by a collection of weightable quasi metrics onX; and a collectionof weights corresponding to the quasi metrics. Understanding the interaction between these structures onXwill eventually lead to some fixed-point theorems for the morphisms in the category of approach spaces, which are called contractions. Existing fixed-point theorems on both monotone and non-monotone maps are obtained as special cases.

scholarly journals Fixed Points and Continuity for a Pair of Contractive Maps with Application to Nonlinear Volterra Integral Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Santosh Kumar
Keyword(s):  
Fixed Point ◽  
Integral Equations ◽  
Existence And Uniqueness ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Volterra Integral Equations ◽  
Discontinuous Mappings ◽  
Contractive Maps ◽  
Uniqueness Of A Solution ◽  
Type Contraction

In this paper, we have established and proved fixed point theorems for the Boyd-Wong-type contraction in metric spaces. In particular, we have generalized the existing results for a pair of mappings that possess a fixed point but not continuous at the fixed point. We can apply this result for both continuous and discontinuous mappings. We have concluded our results by providing an illustrative example for each case and an application to the existence and uniqueness of a solution of nonlinear Volterra integral equations.

scholarly journals SOME GENERALIZATIONS OF KANNAN'S THEOREMS VIA ΣC-FUNCTION AND ITS APPLICATION

2019 ◽  
Vol 24 (4) ◽  
pp. 530-549
Author(s):  
Suprokash Hazra ◽  
Satish Shukla
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Simulation Function ◽  
R Functions

In this article, we go on to discuss various proper extensions of Kannan’s two different fixed point theorems, and introduce the new concept of σc-function, which is independent of the three notions of simulation function, manageable functions, and R-functions. These results are analogous to some well-known theorems, and extend several known results in this literature. An application of the new results to the integral equation is also provided.

scholarly journals Periodic solutions of superlinear and sublinear state-dependent discontinuous differential equations

2021 ◽  
pp. 79-96
Author(s):  
Juan J. Nieto ◽  
José M. Uzal
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Periodic Solutions ◽  
Fixed Point Theorems ◽  
Order Differential Equation ◽  
Point Of View ◽  
Discontinuous Differential Equations ◽  
Planar System ◽  
State Dependent ◽  
Existence Of Periodic Solutions

A classical, second-order differential equation is considered with state-dependent impulses at both the position and its derivative. This means that the instants of impulsive effects depend on the solutions and they are not fixed beforehand, making the study of this problem more difficult and interesting from the real applications point of view. The existence of periodic solutions follows from a transformation of the problem into a planar system followed by a study of the Poincaré map and the use of some fixed point theorems in the plane. Some examples are presented to illustrate the main results.

scholarly journals Fixed point theorems for (φ-ψ) contractions in partially ordered metric-like spaces using new auxiliary functions

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 715-732
Author(s):  
Xiaolan Liu ◽  
Mi Zhou ◽  
Arslan Ansari ◽  
Nawab Hussain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorems ◽  
Case Examples ◽  
Partially Ordered ◽  
Auxiliary Functions

In this paper, we introduce a class of new auxiliary functions and establish certain fixed point theorems under (?-?) contractive conditions in partially ordered metric-like spaces. Our work generalizes some results in the literature and assumes some as particular case. Examples are provided to support the useability of our results.

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