WoS İndeksli Yayınlar Koleksiyonu
Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653
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Article Citation - WoS: 16Citation - Scopus: 14On Multiparametrized Integral Inequalities Via Generalized Α-Convexity on Fractal Set(Wiley, 2025) Xu, Hongyan; Lakhdari, Abdelghani; Jarad, Fahd; Abdeljawad, Thabet; Meftah, BadreddineThis article explores integral inequalities within the framework of local fractional calculus, focusing on the class of generalized alpha-convex functions. It introduces a novel extension of the Hermite-Hadamard inequality and derives numerous fractal inequalities through a novel multiparameterized identity. The primary aim is to generalize existing inequalities, highlighting that previously established results can be obtained by setting specific parameters within the main inequalities. The validity of the derived results is demonstrated through an illustrative example, accompanied by 2D and 3D graphical representations. Lastly, the paper discusses potential practical applications of these findings.Article Variational Approach To a Symmetric Boundary Value Problem Generated by a System of Equations and Separated Boundary Conditions(Wiley, 2024) Ugurlu, EkinThis work provides some information on the eigenvalues and eigenfunctions of a problem which is constructed by a system of equations and symmetric boundary conditions that includes the ordinary second-order Sturm-Liouville boundary value problem. In particular, we show that the problem has an infinite number of discrete eigenvalues with a greatest lower bound and the corresponding eigenfunctions are complete in mean and energy. We introduce the results using the variational approach that enables us to consider only continuous pair functions instead of absolutely continuous pair functions.Article Citation - WoS: 2Citation - Scopus: 4Fixed Points of Proinov Type Multivalued Mappings on Quasimetric Spaces(Wiley, 2022) Karapinar, Erdal; Fulga, Andreea; Yesilkaya, Seher SultanIn this paper, we obtain new results which have not been encountered before in the literature, in multivalued quasimetric spaces, inspired by Proinov type contractions. We use admissible function as proving theorems. We also give an example that supports our theorems.Article Left-Definite System of First-Order Equations Together With Eigenparameter-Dependent Boundary Conditions(Wiley, 2024) Ugurlu, EkinThis paper provides some information on the eigenvalues and eigenfunctions of some left-definite system of first-order differential equations subject to eigenparameter-dependent boundary conditions. Namely, we show that the pair of solutions of the system of equations satisfying some initial conditions exists and is unique, and this pair is analytic in the spectral parameter of order 1/2. We also introduce Lagrange's formula for the left-definite equation. Using some Prufer angels, we investigate oscillation of zeros of eigenfunctions and asymptotics equations for the eigenvalues of the problem. Moreover, we share some ordinary and Frechet derivatives of eigenvalues and eigenfunctions with respect to some elements of data.Article Citation - WoS: 6Citation - Scopus: 20Discussions on Proinov-Cb Mapping on B-Metric Space(Wiley, 2023) Fulga, Andreea; Karapinar, ErdalIn the present paper, we introduce the notion of Proinov-C-b-contraction mapping and we discuss it within the most interesting abstract structure, namely, b-metric spaces. We further take into consideration the necessary conditions to guarantee the existence and uniqueness of fixed points for such mappings, as well as indicate the validity of the main results by providing illustrative examples.Article A New Iteration Scheme for Approximating Common Fixed Points in Uniformly Convex Banach Spaces(Wiley, 2023) Agwu, Imo Kalu; Ishtiaq, Umar; Jarad, Fahd; Saleem, NaeemIn this paper, firstly, we introduce a method for finding common fixed point of L-Lipschitzian and total asymptotically strictly pseudo-non-spreading self-mappings and L-Lipschitzian and total asymptotically strictly pseudo-non-spreading non-self-mappings in the setting of a real uniformly convex Banach space. Secondly, the demiclosedness principle for total asymptotically strictly pseudo-non-spreading non-self-mappings is established. Thirdly, the weak convergence theorems of the proposed method to the common fixed point of the above mappings are proved. Our results improved, extended, and generalized some corresponding results in the literature.Article Citation - WoS: 14Citation - Scopus: 15Solving Integral Equations by Means of Fixed Point Theory(Wiley, 2022) Fulga, A.; Shahzad, N.; Roldan Lopez de Hierro, A. F.; Karapinar, E.One of the most interesting tasks in mathematics is, undoubtedly, to solve any kind of equations. Naturally, this problem has occupied the minds of mathematicians since the dawn of algebra. There are hundreds of techniques for solving many classes of equations, facing the problem of finding solutions and studying whether such solutions are unique or multiple. One of the recent methodologies that is having great success in this field of study is the fixed point theory. Its iterative procedures are applicable to a great variety of contexts in which other algorithms fail. In this paper, we study a very general class of integral equations by means of a novel family of contractions in the setting of metric spaces. The main advantage of this family is the fact that its general contractivity condition can be particularized in a wide range of ways, depending on many parameters. Furthermore, such a contractivity condition involves many distinct terms that can be either adding or multiplying between them. In addition to this, the main contractivity condition makes use of the self-composition of the operator, whose associated theorems used to be more general than the corresponding ones by only using such mapping. In this setting, we demonstrate some fixed point theorems that guarantee the existence and, in some cases, the uniqueness, of fixed points that can be interpreted as solutions of the mentioned integral equations.Article Citation - WoS: 6Citation - Scopus: 9Solving an Integral Equation by Using Fixed Point Approach in Fuzzy Bipolar Metric Spaces(Wiley, 2021) Gnanaprakasam, Arul Joseph; Haq, Absar Ul; Jarad, Fahd; Baloch, Imran Abbas; Mani, GunaseelanThe purpose of this manuscript is to obtain some fixed point results under mild contractive conditions in fuzzy bipolar metric spaces. Our results generalize and extend many of the previous findings in the same approach. Moreover, two examples to support our theorems are obtained. Finally, to examine and strengthen the theoretical results, the existence and uniqueness of the solution to a nonlinear integral equation was studied as a kind of applications.Article Citation - WoS: 11Citation - Scopus: 12Results on Implicit Fractional Pantograph Equations With Mittag-Leffler Kernel and Nonlocal Condition(Wiley, 2022) Panchal, Satish K.; Jarad, Fahd; Almalahi, Mohammed A.In this study, the main focus is on an investigation of the sufficient conditions of existence and uniqueness of solution for two-classess of nonlinear implicit fractional pantograph equations with nonlocal conditions via Atangana-Baleanu-Riemann-Liouville (ABR) and Atangana-Baleanu-Caputo (ABC) fractional derivative with order sigma is an element of 1,2. We introduce the properties of solutions as well as stability results for the proposed problem without using the semigroup property. In the beginning, we convert the given problems into equivalent fractional integral equations. Then, by employing some fixed-point theorems such as Krasnoselskii and Banach's techniques, we examine the existence and uniqueness of solutions to proposed problems. Moreover, by using techniques of nonlinear functional analysis, we analyze Ulam-Hyers (UH) and generalized Ulam-Hyers (GUH) stability results. As an application, we provide some examples to illustrate the validity of our results.Article Shape Preserving Piecewise Knr Fractional Order Biquadratic C<sup>2</Sup> Spline(Wiley, 2021) Riaz, Muhammad Bilal; Jarad, Fahd; Jasim, Hayder Natiq; Enver, Aytekin; Kirmani, Syed Khawar NadeemIn a recent article, a piecewise cubic fractional spline function is developed which produces C-1 continuity to given data points. In the present paper, an interpolant continuity class C-2 is preserved which gives visually pleasing piecewise curves. he behavior of the resulting representations is analyzed intrinsically with respect to variation of the shape control parameters t and s. The data points are restricted to be strictly monotonic along real line.