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Full-Text Articles in Physical Sciences and Mathematics
(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik
(Si10-115) Controllability Results For Nonlinear Impulsive Functional Neutral Integrodifferential Equations In N-Dimensional Fuzzy Vector Space, Murugesan Nagarajan, Kumaran Karthik
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we concentrated to study the controllability of fuzzy solution for nonlinear impulsive functional neutral integrodifferential equations with nonlocal condition in n-dimensional vector space. Moreover, we obtained controllability of fuzzy result for the normal, convex, upper semi-continuous and compactly supported interval fuzzy number. Finally, an example was provided to reveal the application of the result.
On Extended Interpolative Single And Multivalued $F$-Contractions, İsa Yildirim
On Extended Interpolative Single And Multivalued $F$-Contractions, İsa Yildirim
Turkish Journal of Mathematics
The main objective of this paper is to study an extended interpolative single and multivalued Hardy-Rogers type $F$-contractions in complete metric spaces. We prove some fixed point theorems for such mappings. Further, we give an application to integral equations to verify our main results. The results presented in this paper improve the recent works of Karapinar et al. [12] and Mohammadi et al. [16].
Existence And Transportation Inequalities For Fractional Stochastic Differential Equations, Abdelghani Ouahab, Mustapha Belabbas, Johnny Henderson, Fethi Souna
Existence And Transportation Inequalities For Fractional Stochastic Differential Equations, Abdelghani Ouahab, Mustapha Belabbas, Johnny Henderson, Fethi Souna
Turkish Journal of Mathematics
In this work, we establish the existence and uniqueness of solutions for a fractional stochastic differential equation driven by countably many Brownian motions on bounded and unbounded intervals. Also, we study the continuous dependence of solutions on initial data. Finally, we establish the transportation quadratic cost inequality for some classes of fractional stochastic equations and continuous dependence of solutions with respect Wasserstein distance.
On Digital Metric Space Satisfying Certain Rational Inequalities, Krati Shukla
On Digital Metric Space Satisfying Certain Rational Inequalities, Krati Shukla
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we have established some new results by extending some existing theorems in the setting of Digital Metric Space. We also proved some results in Digital Metric Space which were established earlier in the context of Complete Metric Space by different authors.
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Existence Results For A Class Of Boundary Value Problems For Fractional Differential Equations, Abdülkadi̇r Doğan
Turkish Journal of Mathematics
By application of some fixed point theorems, that is, the Banach fixed point theorem, Schaefer's and the Leray-Schauder fixed point theorem, we establish new existence results of solutions to boundary value problems of fractional differential equations. This paper is motivated by Agarwal et al. (Georgian Math. J. 16 (2009) No.3, 401-411).
Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer
Existence Of A Positive Solution For A Singular Fractional Boundary Value Problem With Fractional Boundary Conditions Using Convolution And Lower Order Problems, Jeffrey W. Lyons, Jeffrey T. Neugebauer
Turkish Journal of Mathematics
Existence of a positive solution is shown for two singular two-point fractional boundary value problems with fractional boundary conditions using fixed point theory, lower order problems, and convolution of Green's functions. A nontrivial example is included.
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Some New Uniqueness And Ulam Stability Results For A Class Of Multi-Terms Fractional Differential Equations In The Framework Of Generalized Caputo Fractional Derivative Using The $\Phi$-Fractional Bielecki-Type Norm, Choukri Derbazi, Zidane Baitiche, Michal Feckan
Turkish Journal of Mathematics
In this research article, a novel $\Phi$-fractional Bielecki-type norm introduced by Sousa and Oliveira [23] is used to obtain results on uniqueness and Ulam stability of solutions for a new class of multiterms fractional differential equations in the framework of generalized Caputo fractional derivative. The uniqueness results are obtained by employing Banach' and Perov's fixed point theorems. While the $\Phi$-fractional Gronwall type inequality and the concept of the matrices converging to zero are implemented to examine different types of stabilities in the sense of Ulam-Hyers (UH) of the given problems. Finally, two illustrative examples are provided to demonstrate the validity …
Fuzzy Solutions To Second Order Three Point Boundary Value Problem, Dimplekumar N. Chalishajar, R. Ramesh
Fuzzy Solutions To Second Order Three Point Boundary Value Problem, Dimplekumar N. Chalishajar, R. Ramesh
Applications and Applied Mathematics: An International Journal (AAM)
In this manuscript, the proposed work is to study the existence of second-order differential equations with three point boundary conditions. Existence is proved using fuzzy set valued mappings of a real variable whose values are normal, convex, upper semi continuous and compactly supported fuzzy sets. The sufficient conditions are also provided to establish the existence results of fuzzy solutions of second order differential equations for three point boundary value problem. By using Banach fixed point principle, a new existence theorem of solutions for these equations in the metric space of normal fuzzy convex sets with distance given by the maximum …
Some Results On Fixed Points For Weakly Inward Mappings In Geodesic Metrics Paces, Khalid Abed Jassim, Salwa Salman Abed
Some Results On Fixed Points For Weakly Inward Mappings In Geodesic Metrics Paces, Khalid Abed Jassim, Salwa Salman Abed
Al-Qadisiyah Journal of Pure Science
Geodesic spaces are convex nonlinear spaces. Convexity is a significant tool to generalize some properties of Banach spaces. In this paper, the characterization of weakly inward was extended to CAT(0) spaces and give equivalent condition for the existence of fixed point for multivalued mapping
New Results For Compatible Mappings Of Type A And Subsequential Continuous Mappings, Rajinder Sharma, Vishal Gupta, Mukesh Kushwaha
New Results For Compatible Mappings Of Type A And Subsequential Continuous Mappings, Rajinder Sharma, Vishal Gupta, Mukesh Kushwaha
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we corroborated some common fixed point theorems for two pairs of self mappings by using the impression of compatibility of type A and subsequential continuity (alternatively subcompatiblity and reciprocal continuity) in multiplicative metric spaces (MMS). The proven results are the improved version in a manner that the completeness, closedness and continuity of the mappings are relaxed.
Variants Of Meir-Keeler Fixed Point Theorem And Applications Of Soft Set-Valued Maps, Akbar Azam, Mohammed Shehu Shagari
Variants Of Meir-Keeler Fixed Point Theorem And Applications Of Soft Set-Valued Maps, Akbar Azam, Mohammed Shehu Shagari
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we prove a Meir-Keeler type common fixed point theorem for two mappings for which the range set of the first one is a family of soft sets, called soft set-valued map and the second is a point-to-point mapping. In addition, it is also shown that under some suitable conditions, a soft set-valued map admits a selection having a unique fixed point. In support of the obtained result, nontrivial examples are provided. The novelty of the presented idea herein is that it extends the Meir-Keeler fixed point theorem and the theory of selections for multivalued mappings from the …
A New Solution To The Discontinuity Problem On Metric Spaces, Ufuk Çeli̇k, Ni̇hal Özgür
A New Solution To The Discontinuity Problem On Metric Spaces, Ufuk Çeli̇k, Ni̇hal Özgür
Turkish Journal of Mathematics
We study on the Rhoades' question concerning the discontinuity problem at fixed point for a self-mapping T of a metric space. We obtain a new solution to this question. Our result generalizes some recent theorems existing in the literature and implies the uniqueness of the fixed point. However, there are also cases where the fixed point set of a self-mapping contains more than 1 element. Therefore, by a geometric point of view, we extend the Rhoades' question to the case where the fixed point set is a circle. We also give a solution to this extended version.
On The Weighted Pseudo Almost Periodic Solutions Of Nicholson’S Blowflies Equation, Ramazan Yazgan, Cemil Tunç
On The Weighted Pseudo Almost Periodic Solutions Of Nicholson’S Blowflies Equation, Ramazan Yazgan, Cemil Tunç
Applications and Applied Mathematics: An International Journal (AAM)
This study is concerned with the existence, uniqueness and global exponential stability of weighted pseudo almost periodic solutions of a generalized Nicholson’s blowflies equation with mixed delays. Using some differential inequalities and a fixed point theorem, sufficient conditions were obtained for the existence, uniqueness of at the least a weighted pseudo almost periodic solutions and global exponential stability of this solution. The results of this study are new and complementary to the previous ones can be found in the literature. At the end of the study an example is given to show the accuracy of our results.
On Nonlinear Contractions In New Extended 𝒃-Metric Spaces, Hassen Aydi, Abdelbasset Felhi, Tayyab Kamran, Erdal Karapınar, Muhammad U. Ali
On Nonlinear Contractions In New Extended 𝒃-Metric Spaces, Hassen Aydi, Abdelbasset Felhi, Tayyab Kamran, Erdal Karapınar, Muhammad U. Ali
Applications and Applied Mathematics: An International Journal (AAM)
Very recently, the notion of extended 𝑏-metric spaces was introduced by replacing the modified triangle inequality with a functional triangle inequality and the analog of the renowned Banach fixed point theorem was proved in this new structure. In this paper, continuing in this direction, we further refine the functional inequality and establish some fixed point results for nonlinear contractive mappings in the new setting. A nontrivial example for the new extended 𝑏-metric space is given.
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Value Sets Of Folding Polynomials Over Finite Fields, Ömer Küçüksakalli
Turkish Journal of Mathematics
Let $k$ be a positive integer that is relatively prime to the order of the Weyl group of a semisimple complex Lie algebra $\mf{g}$. We find the cardinality of the value sets of the folding polynomials $P_\mf{g}^k(\mb{x}) \in \Z[\mb{x}]$ of arbitrary rank $n \geq 1$, over finite fields. We achieve this by using a characterization of their fixed points in terms of exponential sums.
The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul
The Large Contraction Principle And Existence Of Periodic Solutions For Infinite Delay Volterra Difference Equations, Paul Eloe, Jaganmohan Jonnalagadda, Youssef Raffoul
Turkish Journal of Mathematics
In this article, we establish sufficient conditions for the existence of periodic solutions of a nonlinear infinite delay Volterra difference equation: $$\Delta x(n) = p(n) + b(n)h(x(n)) + \sum^{n}_{k = -\infty}B(n, k)g(x(k)).$$ We employ a Krasnosel'ski\u{i} type fixed point theorem, originally proved by Burton. The primary sufficient condition is not verifiable in terms of the parameters of the difference equation, and so we provide three applications in which the primary sufficient condition is verified.
On The Affine-Periodic Solutions Of Discrete Dynamical Systems, Hali̇s Can Koyuncuoğlu, Murat Adivar
On The Affine-Periodic Solutions Of Discrete Dynamical Systems, Hali̇s Can Koyuncuoğlu, Murat Adivar
Turkish Journal of Mathematics
Affine periodicity is a generalization of the notion of conventional periodicity and it is a symmetry property for classes of functions. This study is concerned with the existence of $(Q,T)$-affine periodic solutions of discrete dynamical systems. Sufficient conditions for the main results are proposed due to discrete exponential dichotomy and fixed point theory. Obtained results are also implemented for some economical and biological models. In particular cases, our results cover some existing results in the literature for periodic, antiperiodic, or quasiperiodic solutions of difference equations.
The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat
The Localization Theorem For Finite-Dimensional Compact Group Actions, Ali̇ Arslan Özkurt, Mehmet Onat
Turkish Journal of Mathematics
The localization theorem is known for compact $G$-spaces, where $G$ is a compact Lie group. In this study, we show that the localization theorem remains true for finite-dimensional compact group actions, and Borel's fixed point theorem holds not only for torus actions but for arbitrary finite-dimensional compact connected abelian group actions.
The Cohomological Structure Of Fixed Point Set For Pro-Torus Actions On Compact Spaces, Mehmet Onat
The Cohomological Structure Of Fixed Point Set For Pro-Torus Actions On Compact Spaces, Mehmet Onat
Turkish Journal of Mathematics
In this paper, we study the relationships between the cohomological structure of a space and that of the fixed point set of a finite dimensional pro-torus action on the space.
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Existence Of Positive Periodic Solution Of Second-Order Neutral Differential Equations, Tuncay Candan
Turkish Journal of Mathematics
In this work, we consider two types of second-order neutral differential equations and we obtain sufficient conditions for the existence of positive $\om$-periodic solutions for these equations. We employ Krasnoselskii's fixed point theorem for the sum of a completely continuous and a contraction mapping. An example is included to illustrate our results.
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Boundary Sentinels For The Resolution Of A Geometrical Problem, Saida Sandel, Abdelhamid Ayadi
Turkish Journal of Mathematics
The aim of this paper is to estimate the shape of an unknown part of the boundary of a geometrical domain. The identification technique used to estimate this part is the observation of the solution of a diffusion problem on the known part of this boundary. This technique is based on the sentinels theory.
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Some Theorems For A New Type Of Multivalued Contractivemaps On Metric Space, Gonca Durmaz
Turkish Journal of Mathematics
In this paper, taking into account the function $\theta $, we introduce a new type of contraction for multivalued maps on metric space. This new concept includes many known contractions in the literature. We then present some fixed point results for closed and bounded set valued maps on complete metric space. Finally, we provide an example to show the significance of the investigation of this paper.
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Some Fixed Point Theorems For Single Valued Strongly Contractive Mappings In Partially Ordered Ultrametric And Non-Archimedean Normed Spaces, Hamid Mamghaderi, Hashem Parvaneh Masiha, Meraj Hosseini
Turkish Journal of Mathematics
Let $ (X,d,\preceq) $ be a partially ordered ultrametric space and $ f:X\to X $ a single valued mapping. We obtain sufficient conditions for the existence of a fixed point for the strongly contractive mapping $ f $. We also investigate the existence of a fixed point for strongly contractive mappings defined on partially ordered non-Archimedean normed spaces under the same conditions. Finally, we give some examples to discuss the assumptions of the theorems.
A New Aspect To Picard Operators With Simulation Functions, Murat Olgun, Tuğçe Alyildiz, Özge Bi̇çer
A New Aspect To Picard Operators With Simulation Functions, Murat Olgun, Tuğçe Alyildiz, Özge Bi̇çer
Turkish Journal of Mathematics
In the present paper, considering the simulation function, we give a new class of Picard operators on complete metric spaces. We also provide a nontrivial example that shows the aforementioned class properly contains some earlier such classes.
Overall Approach To Mizoguchi--Takahashi Type Fixed Point Results, Gülhan Minak, İshak Altun
Overall Approach To Mizoguchi--Takahashi Type Fixed Point Results, Gülhan Minak, İshak Altun
Turkish Journal of Mathematics
In this work, inspired by the recent technique of Jleli and Samet, we give a new generalization of the well-known Mizoguchi--Takahashi fixed point theorem, which is the closest answer to Reich's conjecture about the existence of fixed points of multivalued mappings on complete metric spaces. We also provide a nontrivial example showing that our result is a proper generalization of the Mizoguchi--Takahashi result.
Existence Of Solutions For Multi-Points Fractional Evolution Equations, Soumia Belarbi, Zoubir Dahmani
Existence Of Solutions For Multi-Points Fractional Evolution Equations, Soumia Belarbi, Zoubir Dahmani
Applications and Applied Mathematics: An International Journal (AAM)
In this paper we study an impulsive fractional evolution equation with nonlinear boundary conditions. Sufficient conditions for the existence and uniqueness of solutions are established. To illustrate our results, an example is presented.
A Generalization Of Banach's Contraction Principle For Some Non-Obviously Contractive Operators In A Cone Metric Space, Yingxin Guo
Turkish Journal of Mathematics
This paper investigates the fixed points for self-maps of a closed set in a space of abstract continuous functions. Our main results essentially extend and generalize some fixed point theorems in cone metric spaces. An application to differential equations is given.
A Fixed Point Theorem For A Compact And Connected Set In Hilbert Space, Hülya Duru
A Fixed Point Theorem For A Compact And Connected Set In Hilbert Space, Hülya Duru
Turkish Journal of Mathematics
Let (H,) be a real Hilbert space and let K be a compact and connected subset of H. We show that every continuous mapping T:K \rightarrow K satisfying a mild condition has a fixed point.
On Characterization Of Metric Completeness, Guo-Jing Jiang
On Characterization Of Metric Completeness, Guo-Jing Jiang
Turkish Journal of Mathematics
We give seven necessary and sufficient conditions for a metric space to be complete.
Fixed Points And Completeness, Z. Liu
Fixed Points And Completeness, Z. Liu
Turkish Journal of Mathematics
We give five necessary and sufficient conditions for a metric space to be complete.