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Some New Fixed and Strict Fixed Point Results in The Set of Multi-Valued Mappings
In this paper, we introduce a new multi valued contraction to generalize the weakly multi valued contractive mappings given by Daffer and Kanako and some consequences studied in this direction. Moreover, we found a necessary and sufficient condition for strict fixed points of mentioned contractions.
NONLINEAR COUPLED COINCIDENCE AND COUPLED FIXED POINT THEOREMS FOR WEAKLY COMPATIBLE MAPPINGS IN PARTIALLY ORDERED PROBABILISTIC METRIC SPACES
In this paper, we introduce the notion of weaker compatibilityof mappings in partially ordered probabilistic metric spaces and use this no-tion to establish a coupled coincidence point results. Very recently DraganDoric [Nonlinear coupled coincidence and coupled xed point theorems for notnecessary commutative contractive mappings in partially ordered probabilisticspaces] proved coupled coincidence point theorems for compatible mappingsin partially ordered probabilistic metric spaces. In this paper we proved re-sults of Dragam under a dierent set of conditions. Precisely, we establishour results by assuming that two mappings in partially ordered probabilisticmetric spaces are weakly compatible. Our results improve and extend a cou-pled xed point theorem due to Bhaskar and Lakshmikantham [T-G.Bhaskar ,V. Lakshmikantham, Fixed point theorems in partially ordered metric spacesand applications, Nolinear Anal, 65(2006) 1379-1393]. An example is given tosupport our result.In this paper, we introduce the notion of weaker compatibilityof mappings in partially ordered probabilistic metric spaces and use this no-tion to establish a coupled coincidence point results. Very recently DraganDoric [Nonlinear coupled coincidence and coupled xed point theorems for notnecessary commutative contractive mappings in partially ordered probabilisticspaces] proved coupled coincidence point theorems for compatible mappingsin partially ordered probabilistic metric spaces. In this paper we proved re-sults of Dragam under a different set of conditions. Our results improve and extend a cou-pled xed point theorem due to Bhaskar and Lakshmikantham. An example is given tosupport our result.
OUSSAEIF TAKI-EDDINE, OUSSAEIF TAKI-EDDINE,
Existence of Positive Solutions for 2n-Order Lidstone Boundary Value Problems with P-Laplacian Operator
In this paper, we establish the existence of positive solutions for $2n^{text {th}}$ order Lidstone boundary value problems with $p$-Laplacian of the form$$(-1)^n[phi_{p}(y^{(2n-2)}(t)-k^2y^{(2n-4)}(t))]''=f(t,y(t)), ~~t in [0, 1], $$$$y^{(2i)}(0)=0=y^{(2i)}(1), for $0leq i leq n-1,$ where $ngeq 2$ and $k>0$ is a constant, by applying Guo--Krasnosel'skii fixed point theorem.
An Application of Fixed Point Theory to A Nonlinear Integral Equation in Banach Spaces
In this paper we propose a new iterative scheme, called the AF iteration process, for approximating the unique solution of a mixed type Volterra-Fredholm functional nonlinear integral equation. We prove in the sense of Berinde \cite{Berin} that our new iterative scheme converges at a rate faster than some of the leading iterative schemes in the literature which have been employed recently to approximate the unique solution of a mixed type Volterra Fredholm functional nonlinear integral equation. We also prove that our new iterative method converges strongly to the unique solution of a mixed type Volterra Fredholm functional nonlinear integral equation. In addition, we give data dependence result for the solution of the nonlinear integral equation which we are considering with the help of our new iterative scheme. Our results improve and unify some well known results in the existing literature.
Convergence of an M-step Iteration Scheme to the Commo Fixed Points of Finite Family of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces
We propose an m-step iteration scheme of hybrid mixed-type for m-total asymptotically nonexpansive self mappings and m-total asymptotically nonexpansive nonself mappings and establish some weak convergence theorems of the scheme to the common fixed point of the mappings in the setting of uniformly convex Banach spaces. In additon, we proved demiclosedness principle for total asymptotically nonexpansive nonself mappings in uniformly convex Banach spaces. Our results extend and genralise the results in [23] and other numerous results currently in literature.
Total Asymptotically Nonexpansive Nonself Mapping
Generalized Monotone Method for System of Riemann-Liouville Fractional Reaction-Diffusion Equations
In this paper, our aim is to obtain the integral representation for the solution of linear Riemann-Liouville reaction-diffusion equations of order $q$ in terms of Green's function where $ 0<q<1 .$ We have developed a generalized monotone method for non-linear weakly coupled system of Riemann-Liouville reaction-diffusion equations when the forcing term is the sum of increasing and decreasing functions. The generalized monotone method yields monotone sequences which converges uniformly and monotonically to coupled minimal and maximal solutions. Under uniqueness assumption, we proved the existence of a unique solution for the non-linear system of Riemann-Liouville reaction-diffusion equations.
Algorithm for Equations of Hammerstein Type and Applications
Equations of Hammerstein type cover large variety of areas and are of much interest to a wide audience due to the fact that they have applications in numerous areas. Suitable conditions are imposed to obtain a strong convergence result for nonlinear integral equations of Hammerstein type with monotone type mappings. A technique which does not involve the assumption of existence of a real constant whose calculation is unclear has been used in this study to obtain the strong convergence result. Moreover, our technique is applied to show the forced oscillations of finite amplitude of a pendulum as a specific example of nonlinear integral equations of Hammerstein type. Numerical example is given for the illustration of the convergence of the sequences of iteration. These are done to demonstrate to our readers that this approach can be applied to problems arising in physical systems.
Fixed points of Nesic type contraction maps in Convex metric spaces
We define Nesic type contraction maps in convex metric spaces and prove the existence and uniqueness of fixed points of these maps in convex metric spaces. Our results extend the results of Nesic ([1], Results on fixed points of asymptotically regular mappings ) from the metric space setting to convex metricspaces.
Measures of Noncompactness on Ω-distance Spaces.
. The aim of this article is to present a new framework for studying measures of noncompactness in G-metric spaces. First, we introduce the concept of Ω-distance space as an Ω-measure of non-compactness on G-metric spaces. Finally, we use our main result to characterize G-metric completeness.
SOME LP− TYPE INEQUALITIES FOR POLAR DERIVATIVE OF A POLYNOMIAL
In this paper, we shall prove some Lpinequalities for the polar derivative of a polynomial having zerosin |z| ≤ k ≤ 1 and thereby obtain generalizations and refinements of an integral inequality due to Barchand Charamet al
Strong Convergence of Monotone Hybrid Algorithms for Maximal Monotone Mappings and Generalized Nonexpansive Mappings
A class of generalized nonexpansive mappings in Banach spaces is considered and a new monotone hybrid algorithm is presented for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping. Under certain conditions on the associated parameters, a strong convergence result is established. Moreover, the obtained result is applied to prove a strong convergence theorem for finding a common element of the zero point set of a maximal monotone operator and the fixed point set of a generalized nonexpansive mapping in a Hilbert space.
Existence and Uniqueness Solutions of System Caputo-type Fractional-Order Boundary Value Problems Using Monotone Iterative Method
In this paper, we investigate the existence and uniqueness solutions of nonlinear boundary value problems for system of Caputo type nonlinear fractional differential equations of the form:\begin{equation*}\label{*}\left\{\begin{array}{c} ^cD_{a^{+}}^{q;\psi} u_{i}(t)=F_{i}(t,u_{1}(t),u_{2}(t)) \quad t\in J=[a,b],\\ \phi(v_{i}(a),v_{i}(b))=0. \end{array} \right. \end{equation*}\\ To develop a monotone iterative technique by introducing upper and lower solutions to Caputo type fractional differential equations with nonlinear boundary conditions. The monotone method yield monotone sequences which converges to uniformly and monotonically to extremal solutions.
Keyword: Riemann-Liouville fractional derivative
The Solutions of Systems of Rational Difference Equations in Terms of Fibonacci Numbers
In this paper, we get the form of the solutions of the following difference equation systems with nonzero real numbers initial conditions z(n+1) =w(n)(z(n-4) + w(n-5))/w(n-5) + z(n-4) - w(n),w(n+1) =z(n-3)(z(n-3) + w(n-4)/2z(n-3) + w(n-4).z(n+1) =w(n)(w(n-5) -z(n-4))/w(n-5)- z(n-4) + w(n),w(n+1) =z(n-3)(w(n-4) -z(n-3)/w(n-4)
Investigating a Coupled System with Riemann-Liouville Fractional Derivative by Modified Monotone Iterative Technique
In recent time, the area of arbitrary order differential equations (AODEs)has been considered very well. Different aspects have been investigated for the saidarea. One of the important and most warm area is devoted to study multiplicityresults along with existence and uniqueness of solutions for the said equations. In thisregard various techniques have been utilized to investigate the said area. Monotoneiterative technique (MIT) coupled with the method of extremal solutions has beenused recently to investigate multiplicity of solutions to some AODEs. In this researchwork, we deal a coupled system of nonlinear AODEs under boundary conditions (BCs)involving Riemann-Liouville fractional derivative by using fixed point theorems dueto Perov’s and Schuader’s to study existence and uniqueness results. Using Perove’sfixed point theorem ensures uniqueness of solution to systems of equations, whileexistence of at least one solution is achieved by Schauder’s fixed point theorem.Then we come across the multiplicity of solutions and establish some criteria for theiterative solutions via using updated type MIT together with the method of upper andlower solutions for the considered system of AODEs. Corresponding to multiplicityresults of solutions, we first establish two sequences of extremal solutions. One of thesequence is monotonically decreasing and converging to lower solution. On the otherhand, the other sequence is monotonically increasing and converging to the uppersolution. In last we give suitable examples to illustrate the main results.
Perov’s and Schuader’s fixed point theorems
The Approximate Solution of COVID-19 Model by Variational Iteration Method
In this work, we investigate a mathematical model of COVID-19 for approximate solution through variation iteration method (VIM). With the help of the said technique, we develop an algorithm to compute series type solution to the proposed problem. Then using some real values for the parameters and initial data, we compute few terms approximate solutions corresponding to different compartment. With the help of Mathematica, we also plot our approximate solutions for different compartment graphically.
Approximating endpoints of multi-valued generalized $\alpha$-nonexpansive mappings in Banach spaces
In this paper, we study endpoints of multi-valued generalized $\alpha$-nonexpansive mappings in Banach spaces. Under some appropriate assumptions, we prove that the sequence of modified Agarwal-O'Rega-Sahu iterative process defined by Abdeljawad et al. (2020) converges strongly to an endpoint of a multi-valued generalized $\alpha$-nonexpansive mappings. We also give an illustrate example. Our results are new and extend the corresponding results of the current literature.
generalized $alpha$-nonexpansive mapping
A Split Common Fixed Point and Null Point Problem for Lipschitzian Quasi Pseudocontractive Mappings in Hilbert Spaces
A split common fixed point and null point problem (SCFPNPP) which includes the splitcommon fixed point problem, the split common null point problem and other problems related to the fixed pointproblem and the null point problem is studied. We introduce a Halpern--Ishikawa type algorithm for studying the split common fixed point and null point problem for Lipschitzian quasi pseudocontractive operators and maximal monotone operators in real Hilbert spaces. Moreover, we establish a strong convergence results under some suitable conditions and reduce our main result to above-mentioned problems. We give numerical result to demonstrate the convergence of our algorithms and compare rate of convergence some iterative algorithms. Finally, we applied the study to split feasibility problem (FEP), split equilibrium problem (SEP), split variational inequality problem (SVIP) and split optimization problem (SOP).
The Study Of Manageable Functions And Approximate Fixed Point Property With Their Application
In this work, we want to investigate and improve the concept of manageable functions and M_n (R)-contractions in order to extend the theory of multi-valued contractions and fixed point results
Antonio Francisco Roldan Lopez de Hierro
Convergence of general composite iterative method for infinite family of nonexpansive mappings in Hilbert spaces
In this paper by using W_n -mapping, we introduce a composite iterative method for finding a commonfixed point for infinite family of nonexpansive mappings and a solution of a certain variational inequality.Furthermore, the strong convergence of the proposed iterative method is established. Finally, some sim-ulation examples are presented. Our results improve and extend the previous results. c ⃝2016 All rightsreserved.
In this paper, we assign a linear operator to the action of an amenable group on a compact metric space. Then we extract the entropy of the action in terms of the eigenvalues of the operator. In this way we present a spectral representation of the entropy of action of amenable groups.
We introduced a new class of multi-valued mappings, called P-KKM mappings, which generalized the notationof R-KKM maps of Raj and Somasundaram [KKM-type theorem for best proximity points, AppliedMathematics Letters, 25 (2012), 496-499] and appropriate to best proximity theory. An analog version ofKKM property and a common fixed point theorem is also proved.
Fixed Point And Coupled Fixed Point Theorems For Multivalued Contractions With Respect To The Excess Functional
In this paper, we will consider the coupled fixed point problem for a multi-valued operator satisfying acontraction condition with respect to the excess functional in b-metric spaces. The approach is basedon a fixed point theorem for a multi-valued operator in the setting of a b-metric space. On one hand,we will consider the problem of the existence of the solutions and on the other hand, data dependence,well-posedness, Ulam-Hyers stability and limit shadowing property of the coupled fixed point problem arediscussed. Some applications to a system of integral inclusions and to a multi-valued periodic boundaryvalue problem are also given. c
multi-valued periodic boundary value problem
Some common fixed point theorems for single valued mappings in G-ultrametric spaces
The purpose of this paper is to prove some common fixed point theorems for a single valued stronglycontractive mapping having a pair of maps on a spherically complete G-ultrametric space. c ⃝2016 All rightsreserved.
spherically complete G-ultrametric space
On the existence of solution for a singular Riemann-Liouville fractional differential system by using measure of non-compactness
We investigate the existence of solution for a singular fractional differential system with Riemann-Liouvilleintegral boundary conditions by using the measure of non-compactness.
We investigate the existence of solution for a singular fractional differential system with Riemann-Liouville
integral boundary conditions by using the measure of non-compactness
Best Proximity Point for Presic Type Mappings on Metric Spaces
In this paper, we define the best proximity point for Preˇ si´ c type non-self mappings and prove some bestproximity point theorems in complete metric spaces. c
Some Inequalities for the Polar Derivative of a Polynomial Having S-Fold Zeros at the Origin
Let $P(z)$ be a polynomial of degree $n$ having all its zeros in $|z|\leq 1$ then for all $(\alpha_i)^t_{i=1}\in \mathbb{C}$ with $|\alpha_i|\geq 1, 1\leq i\leq t<n$, it was proved by Jain[V. K. Jain, Generalization of an inequality involving maximum moduli of a polynomial and its polar derivative, Bull Math Soc Sci Math Roum Tome. 98, 67–74 (2007)] that\begin{align*}\max\limits_{|z|=1}|D_{\alpha_t}...D_{\alpha_2}D_{\alpha_1}P(z)|\geq\frac{n_t}{2^t}\left[A_{\alpha_t}\max\limits_{|z|=1}|P(z)|+\left( 2^t\prod\limits_{i=1}^{t}|\alpha_i|- A_{\alpha_t}\right)\min\limits_{|z|=1}|P(z)| \right].\end{align*}where $n_t=n(n-1)...(n-t+1)$ and $A_{\alpha_t}=(|\alpha_1|-1)(|\alpha_2|-1)...(|\alpha_t|-1)$. In this paper, we generalize this and some other results.
Coincidence Points with φ-Contractions in Partially Ordered Fuzzy Metric Spaces
In this paper our main result is a coupled coincidence point theorem for a compatible pairin a fuzzy metric space with a partial ordering under the assumption of a new coupled contraction inequality which involves a recently introduced control function which is a generalization ofmany such functions previously used in literatures. The proof depends on a lemma in which weprove a condition for simultaneous holding of Cauchy criteria for two sequences. We use H-typet-norms in this paper in order to utilize the equi-continuity of the t-norm iterates in the proofof the lemma. The contraction inequality also involves another function which is borrowed froma recent work, there is a partial ordering defined on the fuzzy metric space. There are severalcorollaries of the main theorem. An illustrative example is given.
Isolation Effect on Age-Stratified Compartmental Model of the COVID-19
Focusing on the dynamics of the most recent outbreak of COVID-19, we formulate an age distributed model with five different components in terms of nonlinear partial differential equations. The model has been analyzed by studying the stability of the equilibrium points and their reproduction number. To explore the disease effect on different ages more efficiently, we apply the recent estimated data in the formulated model and analyze it numerically. From the model’s numerical solution profiles, we observed more susceptibility and infection among the older population. Also studied the effectiveness of isolation in controlling illness and death.
On New Fixed Point Results for Some Classes of Enriched Mappings in N-Banach Spaces
We introduce the concepts of enriched n-contraction mapping, enriched n-Chatterjea mapping and enriched n-Kannan mapping in linear n-normed space. We prove some fixed point theorems for such mappings using Krasnoselsij iteration process in n-Banach spaces. The results presented in this paper improve the recent works of Berinde and Pacurar (J. Fixed Point Theory Appl. (2020) 22-38), Berinde and Pacurar (Preprint, arXiv:1909.03494) and Berinde and Pacurar (Preprint, arXiv:1909.02379, 2019) to linear n-normed spaces.
Convergence Theorems for Monotone Generalized α-Nonexpansive Mappings in Ordered Banach Space by a New Four-Step Iteration Process with Application
We introduce a new four-step iterative algorithm and show that the new algorithm converges faster than a number of existing iterative algorithms for contraction mappings. We prove strong and weak convergence results for approximating fixed points of monotone generalized α-nonexpansive mappings. Further, we utilize our proposed algorithm to solve Split FeasibilityProblem (SFP). Our result complements, extends and generalizes some existing results in literature.