scholarly journals A solution to nonlinear Volterra integro-dynamic equations via fixed point theory

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5331-5343 ◽  
Author(s):  
Rezan Sevinik-Adıguzel ◽  
Erdal Karapınar ◽  
İnci Erhan
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Dynamic Equations ◽  
Comparison Function ◽  
Contractive Condition ◽  
Uniqueness Of Solutions

In this paper we discuss the existence and uniqueness of solutions of a certain type of nonlinear Volterra integro-dynamic equations on time scales. We investigate the problem in the setting of a complete bmetric space and apply a fixed point theorem with a contractive condition involving b-comparison function. We use the theoremto show the existence of a unique solution of some particular integro-dynamic equations.

scholarly journals Semicompatibility and fixed point theorems in an unboundedD-metric space

2005 ◽  
Vol 2005 (5) ◽  
pp. 789-801
Author(s):  
Bijendra Singh ◽  
Shishir Jain ◽  
Shobha Jain
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Space ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Restricted Domain

Rhoades (1996) proved a fixed point theorem in a boundedD-metric space for a contractive self-map with applications. Here we establish a more general fixed point theorem in an unboundedD-metric space, for two self-maps satisfying a general contractive condition with a restricted domain ofxandy. This has been done by using the notion of semicompatible maps inD-metric space. These results generalize and improve the results of Rhoades (1996), Dhage et al. (2000), and Veerapandi and Rao (1996). These results also underline the necessity and importance of semicompatibility in fixed point theory ofD-metric spaces. All the results of this paper are new.

scholarly journals Common fixed point theorem for four mappings satisfying generalized weak contractive condition

Filomat ◽  
2010 ◽  
Vol 24 (2) ◽  
pp. 1-10 ◽  
Author(s):  
Mujahid Abbas ◽  
Dragan Djoric
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Common Fixed Point ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Applied Mathematics ◽  
Point Theory ◽  
Contractive Condition ◽  
Mathematics Subject Classifications ◽  
Common Fixed Point Theorem

Contractive conditions introduced in (Q. Zhang and Y. Song, Fixed point theory for generalized ?-weak contraction, Appl. Math. Lett. 22(2009), 75-78) and (D. Djoric, Common fixed point for generalized (?, ?)-weak contractions, Applied Mathematics Letters, 22(2009), 1896-1900) are employed to obtain a new common fixed point theorem for four maps. Our result substantially generalizes comparable results in the literature. 2010 Mathematics Subject Classifications. 47H10. .

scholarly journals On the Power of Simulation and Admissible Functions in Metric Fixed Point Theory

2017 ◽  
Vol 2017 ◽  
pp. 1-7 ◽  
Author(s):  
Areej S. S. Alharbi ◽  
Hamed H. Alsulami ◽  
Erdal Karapinar
Keyword(s):  
Fixed Point ◽  
Existence And Uniqueness ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Admissible Function ◽  
Point Theory ◽  
Contractive Condition ◽  
Simulation Function ◽  
The Given ◽  
Admissible Functions

We investigate the existence and uniqueness of certain operators which form a new contractive condition via the combining of the notions of admissible function and simulation function contained in the context of completeb-metric spaces. The given results not only unify but also generalize a number of existing results on the topic in the corresponding literature.

scholarly journals RIEMANN–LIOUVILLE FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS WITH FRACTIONAL NONLOCAL MULTI-POINT BOUNDARY CONDITIONS

Fractals ◽  
2021 ◽  
pp. 2240002
Author(s):  
BASHIR AHMAD ◽  
BADRAH ALGHAMDI ◽  
RAVI P. AGARWAL ◽  
AHMED ALSAEDI
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Weighted Space ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Fractional Integrals ◽  
Existence Theory ◽  
Uniqueness Of Solutions

In this paper, we investigate the existence and uniqueness of solutions for Riemann–Liouville fractional integro-differential equations equipped with fractional nonlocal multi-point and strip boundary conditions in the weighted space. The methods of our study include the well-known tools of the fixed point theory, which are commonly applied to establish the existence theory for the initial and boundary value problems after converting them into the fixed point problems. We also discuss the case when the nonlinearity depends on the Riemann–Liouville fractional integrals of the unknown function. Numerical examples illustrating the main results are presented.

scholarly journals Multi-valued F-contractions and the solutions of certain functional and integral equations

Filomat ◽  
2013 ◽  
Vol 27 (7) ◽  
pp. 1259-1268 ◽  
Author(s):  
Margherita Sgroi ◽  
Calogero Vetro
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Ordered Metric Spaces ◽  
Complete Metric Spaces ◽  
Banach Contraction

Wardowski [Fixed Point Theory Appl., 2012:94] introduced a new concept of contraction and proved a fixed point theorem which generalizes Banach contraction principle. Following this direction of research, we will present some fixed point results for closed multi-valued F-contractions or multi-valued mappings which satisfy an F-contractive condition of Hardy-Rogers-type, in the setting of complete metric spaces or complete ordered metric spaces. An example and two applications, for the solution of certain functional and integral equations, are given to illustrate the usability of the obtained results.

Unique Solution for Multi-point Fractional Integro-Differential Equations

2020 ◽  
Vol 21 (2) ◽  
pp. 219-226
Author(s):  
Chengbo Zhai ◽  
Lifang Wei
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Unique Solution ◽  
Existence And Uniqueness ◽  
Iterative Sequence ◽  
Point Boundary ◽  
Uniqueness Of Solutions

AbstractWe study a fractional integro-differential equation subject to multi-point boundary conditions: $$\left\{\begin{array}{l} D^\alpha_{0^+} u(t)+f(t,u(t),Tu(t),Su(t))=b,\ t\in(0,1),\\u(0)=u^\prime(0)=\cdots=u^{(n-2)}(0)=0,\\ D^p_{0^+}u(t)|_{t=1}=\sum\limits_{i=1}^m a_iD^q_{0^+}u(t)|_{t=\xi_i},\end{array}\right.$$where $\alpha\in (n-1,n],\ n\in \textbf{N},\ n\geq 3,\ a_i\geq 0,\ 0<\xi_1<\cdots<\xi_m\leq 1,\ p\in [1,n-2],\ q\in[0,p],b>0$. By utilizing a new fixed point theorem of increasing $\psi-(h,r)-$ concave operators defined on special sets in ordered spaces, we demonstrate existence and uniqueness of solutions for this problem. Besides, it is shown that an iterative sequence can be constructed to approximate the unique solution. Finally, the main result is illustrated with the aid of an example.

scholarly journals A fixed point theorem for a new class of set-valued mappings in R-complete (not necessarily complete) metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3875-3884 ◽  
Author(s):  
Hamid Baghani ◽  
Maryam Ramezani
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Contractive Condition ◽  
Complete Metric Spaces ◽  
New Class ◽  
Set Valued Mappings

In this paper, firstly, we introduce the notion of R-complete metric spaces. This notion let us to consider fixed point theorem in R-complete instead of complete metric spaces. Secondly, as motivated by the recent work of Amini-Harandi (Fixed Point Theory Appl. 2012, 2012:215), we explain a new generalized contractive condition for set-valued mappings and prove a fixed point theorem in R-complete metric spaces which extends some well-known results in the literature. Finally, some examples are given to support our main theorem and also we find the existence of solution for a first-order ordinary differential equation.

scholarly journals A Note on Extended Z-Contraction

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 195 ◽  
Author(s):  
Maryam A. Alghamdi ◽  
Selma Gulyaz-Ozyurt ◽  
Erdal Karapınar
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Existence And Uniqueness ◽  
General Framework ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Auxiliary Function ◽  
Common Fixed Points ◽  
Simulation Function ◽  
Common Fixed Point Theorem

In this article, we aim to evaluate and merge the as-scattered-as-possible results in fixed point theory from a general framework. In particular, we considered a common fixed point theorem via extended Z-contraction with respect to ψ -simulation function over an auxiliary function ξ in the setting of b-metric space. We investigated both the existence and uniqueness of common fixed points of such mappings. We used an example to illustrate the main result observed. Our main results cover several existing results in the corresponding literature.

scholarly journals New Fixed Point Theorem on Triple Controlled Metric Type Spaces with Applications to Volterra–Fredholm Integro-Dynamic Equations

Axioms ◽  
2022 ◽  
Vol 11 (1) ◽  
pp. 19
Author(s):  
Kalpana Gopalan ◽  
Sumaiya Tasneem Zubair ◽  
Thabet Abdeljawad ◽  
Nabil Mlaiki
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Dynamic Equation ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Initial Value ◽  
Uniqueness Of Solutions ◽  
Research Article ◽  
Type Spaces

The objective of the research article is two-fold. Firstly, we present a fixed point result in the context of triple controlled metric type spaces with a distinctive contractive condition involving the controlled functions. Secondly, we consider an initial value problem associated with a nonlinear Volterra–Fredholm integro-dynamic equation and examine the existence and uniqueness of solutions via fixed point theorem in the setting of complete triple controlled metric type spaces. Furthermore, the theorem is applied to illustrate the existence of a unique solution to an integro-dynamic equation.

scholarly journals An Investigation of an Integral Equation Involving Convex–Concave Nonlinearities

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2372
Author(s):  
Ravi P. Agarwal ◽  
Mohamed Jleli ◽  
Bessem Samet
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Unique Solution ◽  
Positive Solutions ◽  
Numerical Algorithm ◽  
Existence And Uniqueness ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Partial Ordering ◽  
Picard Iterations

We investigate the existence and uniqueness of positive solutions to an integral equation involving convex or concave nonlinearities. A numerical algorithm based on Picard iterations is provided to obtain an approximation of the unique solution. The main tools used in this work are based on partial-ordering methods and fixed-point theory. Our results are supported by examples.

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