scholarly journals On a Volterra Integral Equation with Delay, via w-Distances

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2341
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Volterra Integral Equation ◽  
Type Theorem ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Operator Technique ◽  
Uniqueness Of Solutions ◽  
Picard Operator ◽  
Contraction Theorem ◽  
Equation With Delay

The paper deals with a Volterra integral equation with delay. In order to apply the w-weak generalized contraction theorem for the study of existence and uniqueness of solutions, we rewrite the equation as a fixed point problem. The assumptions take into account the support of w-distance and the complexity of the delay equation. Gronwall-type theorem and comparison theorem are also discussed using a weak Picard operator technique. In the end, an example is provided to support our results.

A viscosity-type algorithm for an infinitely countable family of (f,g)-generalized k-strictly pseudononspreading mappings in CAT(0) spaces

Analysis ◽  
2020 ◽  
Vol 40 (1) ◽  
pp. 19-37 ◽  
Author(s):  
Kazeem O. Aremu ◽  
Hammed Abass ◽  
Chinedu Izuchukwu ◽  
Oluwatosin T. Mewomo
Keyword(s):  
Integral Equation ◽  
Fixed Point Problem ◽  
Countable Family ◽  
Inclusion Problem ◽  
Point Problem ◽  
Monotone Inclusion ◽  
Nonlinear Volterra Integral Equation ◽  
Common Solution ◽  
Type Algorithm ◽  
Monotone Inclusion Problem

AbstractIn this paper, we propose a viscosity-type algorithm to approximate a common solution of a monotone inclusion problem, a minimization problem and a fixed point problem for an infinitely countable family of {(f,g)}-generalized k-strictly pseudononspreading mappings in a {\mathrm{CAT}(0)} space. We obtain a strong convergence of the proposed algorithm to the aforementioned problems in a complete {\mathrm{CAT}(0)} space. Furthermore, we give an application of our result to a nonlinear Volterra integral equation and a numerical example to support our main result. Our results complement and extend many recent results in literature.

scholarly journals Several Fixed-Point Theorems for F -Contractions in Complete Branciari b -Metric Spaces and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Lili Chen ◽  
Shuai Huang ◽  
Chaobo Li ◽  
Yanfeng Zhao
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Related Result ◽  
Fixed Point Problem ◽  
Common Fixed Points ◽  
Point Problem ◽  
Well Posedness ◽  
Uniqueness Of Solutions

In this paper, we prove the existence and uniqueness of fixed points for F -contractions in complete Branciari b -metric spaces. Furthermore, an example for supporting the related result is shown. We also present the concept of the weak well-posedness of the fixed-point problem of the mapping T and discuss the weak well-posedness of the fixed-point problem of an F -contraction in complete Branciari b -metric spaces. Besides, we investigate the problem of common fixed points for F -contractions in above spaces. As an application, we apply our main results to solving the existence and uniqueness of solutions for a class of the integral equation and the dynamic programming problem, respectively.

scholarly journals Existence and Uniqueness of the Solution for an Integral Equation with Supremum, via w-Distances

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1554 ◽  
Author(s):  
Veronica Ilea ◽  
Diana Otrocol
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Existence And Uniqueness ◽  
Stability Result ◽  
Fixed Point Problem ◽  
Comparison Theorems ◽  
Point Problem ◽  
Existence And Uniqueness Results ◽  
Uniqueness Results ◽  
Uniqueness Of The Solution

Following the idea of T. Wongyat and W. Sintunavarat, we obtain some existence and uniqueness results for the solution of an integral equation with supremum. The paper ends with the study of Gronwall-type theorems, comparison theorems and a result regarding a Ulam–Hyers stability result for the corresponding fixed point problem.

scholarly journals Iterative Algorithms for a Generalized System of Mixed Variational-Like Inclusion Problems and Altering Points Problem

2020 ◽  
Vol 8 (2) ◽  
pp. 549-564
Author(s):  
Monairah Alansari ◽  
Mohd Akram ◽  
Mohd. Dilshad
Keyword(s):  
Convergence Analysis ◽  
Iterative Algorithms ◽  
Fixed Point Problem ◽  
Monotone Mappings ◽  
Point Problem ◽  
Operator Technique ◽  
Inclusion Problems ◽  
Common Solution ◽  
Generalized System ◽  
Resolvent Operator Technique

In this article, we introduce and study a generalized system of mixed variational-like inclusion problems involving αβ-symmetric η-monotone mappings. We use the resolvent operator technique to calculate the approximate common solution of the generalized system of variational-like inclusion problems involving αβ-symmetric η-monotone mappings and a fixed point problem for nonlinear Lipchitz mappings. We study strong convergence analysis of the sequences generated by proposed Mann type iterative algorithms. Moreover, we consider an altering points problem associated with a generalized system of variational-like inclusion problems. To calculate the approximate solution of our system, we proposed a parallel S-iterative algorithm and study the convergence analysis of the sequences generated by proposed parallel S-iterative algorithms by using the technique of altering points problem. The results presented in this paper may be viewed as generalizations and refinements of the results existing in the literature.

Three-Step Iterative Method for Completely Generalized Set-Valued Strongly Nonlinear Quasi-Variational Inclusions

2013 ◽  
Vol 710 ◽  
pp. 598-602
Author(s):  
Bao Di Fang
Keyword(s):  
Iterative Method ◽  
Monotone Mapping ◽  
Maximal Monotone ◽  
Fixed Point Problem ◽  
Variational Inclusion ◽  
Point Problem ◽  
Operator Technique ◽  
Variational Inclusions ◽  
Strongly Nonlinear ◽  
Resolvent Operator Technique

In this paper, we introduce and study a new class of completely generalized set-valued strongly nonlinear variational inclusions in Hilbert spaces and establish the equivalence between this variational inclusion and the fixed-point problem by using the resolvent operator technique for maximal monotone mapping. We construct a new three-step iterative algorithm and show the existence of solution for this variational inclusion and the convergence of the iterative method generated by the iterative method.

scholarly journals A fixed point approach to the solution of singular fractional differential equations with integral boundary conditions

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Kalaivani Chandran ◽  
Kalpana Gopalan ◽  
Sumaiya Tasneem Zubair ◽  
Thabet Abdeljawad
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Integral Boundary Conditions ◽  
Fixed Point Problem ◽  
Point Problem ◽  
List Type ◽  
Uniqueness Of Solutions ◽  
Integral Boundary ◽  
Fractional Differential

AbstractIn this article, we first demonstrate a fixed point result under certain contraction in the setting of controlled b-Branciari metric type spaces. Thereafter, we specifically consider a following boundary value problem (BVP) for a singular fractional differential equation of order α: $$ \begin{aligned} &{}^{c}D^{\alpha }v(t) + h \bigl(t,v(t) \bigr) = 0,\quad 0< t< 1, \\ &v''(0) = v'''(0) = 0, \\ &v'(0) = v(1) = \beta \int _{0}^{1} v(s) \,ds, \end{aligned} $$ D α c v ( t ) + h ( t , v ( t ) ) = 0 , 0 < t < 1 , v ″ ( 0 ) = v ‴ ( 0 ) = 0 , v ′ ( 0 ) = v ( 1 ) = β ∫ 0 1 v ( s ) d s , where $3<\alpha <4$ 3 < α < 4 , $0<\beta <2$ 0 < β < 2 , ${}^{c}D^{\alpha }$ D α c is the Caputo fractional derivative and h may be singular at $v = 0$ v = 0 . Eventually, we investigate the existence and uniqueness of solutions of the aforementioned boundary value problem of order α via a fixed point problem of an integral operator.

Uniqueness of solutions for a class of non-linear Volterra integral equations with convolution kernel

1989 ◽  
Vol 106 (3) ◽  
pp. 547-552 ◽  
Author(s):  
P. J. Bushell ◽  
W. Okrasinski
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Convolution Kernel ◽  
Qualitative Behaviour ◽  
Uniqueness Of Solutions ◽  
Linear Diffusion ◽  
Non Linear ◽  
Linear Volterra Integral Equations ◽  
Image Position

The non-linear Volterra integral equationhas been studied recently in connection with non-linear diffusion and percolation problems [4, 6, 10]. The existence, uniqueness and qualitative behaviour of non-negative, non-trivial solutions are the questions of physical interest.

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