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Article Existence, Uniqueness and Successive Approximations for (λ, Ψ)-Hilfer Fractional Differential Equations(Univ Politehnica Bucharest, Sci Bull, 2024) Krim, Salim; Salim, Abdelkrim; Benchohra, Mouffak; Karapinar, ErdalThe focus of this paper is on investigating a particular type of nonlinear (lambda, psi)-Hilfer fractional differential equations, and analyzing their existence results. Our approach involves utilizing Banach's fixed point theorem, and we also explore the global convergence of successive approximations to provide additional insights into the topic. To further illustrate our findings, we provide some examples that supplement our main results.Article Citation - WoS: 1Citation - Scopus: 1On the Determination of a Complex Finite Jacobi Matrix From Spectral Data(Univ Politehnica Bucharest, Sci Bull, 2015) Guseinov, Gusein Sh; MathematicsIn this paper, we study the necessary and sufficient conditions for solvability of an inverse spectral problem for finite order complex Jacobi matrices (tri-diagonal symmetric matrices with complex entries). The problem is to reconstruct the complex Jacobi matrix from the spectral data consisting of eigenvalues and normalizing numbers of this matrix. An explicit procedure of reconstruction of the matrix from the spectral data is given.Article Citation - WoS: 5Citation - Scopus: 7On Jaggi Type Contraction Mappings(Univ Politehnica Bucharest, Sci Bull, 2018) Karapinar, Erdal; MathematicsBy a work of Jaggi, it is known that the existence of certain inequalities for continuous maps over metric spaces implies the existence and uniqueness of fixed points. In this paper, we show that if p denotes a partial metric, the existence of a rational form of type p(Tt,Ts) <= a(1) p(t,Tt).p(s,Ts)/d(t,s)+a(2)p(t,s) for some a 1 and a 2 with a(1) + a(2) < 1 for a continuous map T over a partial metric space leads to the same conclusions, that is, the existence and uniqueness of fixed points.Article Citation - WoS: 33Citation - Scopus: 34Iterative Approximation of Fixed Points for Presic Type f-contraction Operators(Univ Politehnica Bucharest, Sci Bull, 2016) Abbas, M.; Karapınar, Erdal; Berzig, M.; Nazir, T.; Karapinar, E.; Karapınar, Erdal; Mathematics; Mathematics; MathematicsWe study the convergence of the Presic type k-step iterative process for a class of operators f : X-k -> X satisfying Presic type F-contractive condition in the setting of metric spaces. As an applications of the result presented herein, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.Article Citation - WoS: 7ON (α-φ)-MEIR-KEELER CONTRACTIONS ON PARTIAL HAUSDORFF METRIC SPACES(Univ Politehnica Bucharest, Sci Bull, 2018) Chen, Chi-Ming; Karapinar, Erdal; O'Regan, DonalIn this note we introduce the concept of a (alpha-phi)-Meir-Keeler contraction for multi-valued mappings and we investigate the existence of fixed points of such mappings in a complete partial metric space. Our results generalize, extend and unify several recent fixed point results.
