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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14411/18

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Author: search.filters.author.Aksoy, Umit

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Now showing 1 - 10 of 21
  • Article
    Citation - WoS: 1
    Citation - Scopus: 1
    Several Outcomes of Fixed-Point Theory in Interpolative Metric Spaces
    (Univ Politecnica Valencia, Editorial UPV, 2025-10-01) Karapinar, Erdal; Kadioglu, Kaan; Turkmenel, Merve Gulcin; Aksoy, Umit
    This paper aims to generalize and improve the recent fixed-point theorems in the setting of interpolative metric spaces. More precisely, we investigate the existence and uniqueness of the fixed-point for certain operators of the C<acute accent>iric<acute accent>-Reich-Rus-type, via admissible mapping in the context of interpolative metric spaces.
  • Article
    On a Boundary Value Problem for a Class of Second-Order Complex Partial Differential Equations
    (Univ Simon Bolivar, 2023) Aksoy, Umit; Celebi, Ahmet Okay
    In this article, a boundary value problem for a second-order complex partial differential equation whose main part is the Laplacian, is introduced and its solvability is discussed by reduction of the problem into the Schwarz problem for a first-order equation. The condition for solvability is presented and an estimate for the unique solution is provided.
  • Article
    Citation - WoS: 70
    FIXED POINTS OF GENERALIZED α-ADMISSIBLE CONTRACTIONS ON <i>b</i>-METRIC SPACES WITH AN APPLICATION TO BOUNDARY VALUE PROBLEMS
    (Yokohama Publ, 2016) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.
    A general class of alpha-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations.
  • Article
    Citation - WoS: 150
    Citation - Scopus: 171
    On the Solutions of Fractional Differential Equations Via Geraghty Type Hybrid Contractions
    (Ministry Communications & High Technologies Republic Azerbaijan, 2021) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Aksoy, Umit; Aksoy, Ümit; Karapinar, Erdal; Karapınar, Erdal; Erhan, Inci M.; Erhan, İnci; Sevinik Adıgüzel, Rezan; Aksoy, Ümit; Karapınar, Erdal; Erhan, İnci; Mathematics; Mathematics; Mathematics
    The aim of this article is twofold. Firstly, to study fixed points of mappings on b metric spaces satisfying a general contractive condition called Geraghty type hybrid contraction. Secondly, to apply the theoretical results to the problem of existence and uniqueness of solutions of boundary value problems with integral boundary conditions associated with a certain type of nonlinear fractional differential equations. The conditions for the existence of fixed points for Geraghty type hybrid contractions are determined and several consequences of the main results are deduced. Some examples on boundary value problems for nonlinear fractional differential equations of order 3 < alpha <= 4 are provided, where the existence and uniqueness of solutions are shown by using Geraghty type contractions.
  • Article
    Citation - WoS: 12
    Citation - Scopus: 15
    Schwarz Problem for Higher-Order Complex Partial Differential Equations in the Upper Half Plane
    (Wiley-v C H verlag Gmbh, 2019-01-04) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay
    Linear and nonlinear elliptic complex partial differential equations of higher-order are considered under Schwarz conditions in the upper-half plane, Firstly, using the integral representations for the solutions of the inhomogeneous polyanalytic equation with Schvvarz conditions, a class of integral operators is introduced together with some of their properties. Then, these operators are used to transform the problem for linear equations into singular integral equations. In the case of nonlinear equations such a transformation yields a system of integro-differential equations. Existence of the solutions of the relevant boundary value problems for linear and nonlinear equations are discussed via Fredholm theory and fixed point theorems, respectively.
  • Article
    Citation - WoS: 10
    Citation - Scopus: 10
    Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem
    (Taylor & Francis Ltd, 2018-08-14) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay
    According to an observation of A.V. Bitsadze from 1948 the Dirichlet problem for bianalytic functions is ill-posed. A natural boundary condition for the polyanalytic operator, however, is the Schwarz condition. An integral representation for the solutions in the unit disc to the inhomogeneous polyanalytic equation satisfying Schwarz boundary conditions is known. This representation is extended here to any simply connected plane domain having a harmonic Green function. Some other boundary value problems are investigated with some Dirichlet and Neumann conditions illuminating that just the Schwarz problem is a natural boundary condition for the Bitsadze operator.
  • Article
    Citation - WoS: 8
    Citation - Scopus: 9
    Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem Revisited
    (Taylor & Francis Ltd, 2020-02-24) Aksoy, Umit; Begehr, Heinrich; Celebi, A. Okay
    The extension of the Schwarz representation formula to simply connected domains with harmonic Green function and its polyanalytic generalization is not valid in general. They do hold only for certain domains.
  • Article
    Citation - WoS: 3
    Citation - Scopus: 4
    On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation
    (Taylor & Francis Ltd, 2020-03-24) Aksoy, Umit; Erhan, Inci M.; Fulga, Andreea; Karapinar, Erdal
    In this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.
  • Article
    Citation - WoS: 206
    Citation - Scopus: 183
    On the Solution of a Boundary Value Problem Associated With a Fractional Differential Equation
    (Wiley, 2020-06-23) Sevinik Adiguzel, Rezan; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.; Adiguzel, Rezan Sevinik
    The problem of the existence and uniqueness of solutions of boundary value problems (BVPs) for a nonlinear fractional differential equation of order 2<alpha <= 3 is studied. The BVP is transformed into an integral equation and discussed by means of a fixed point problem for an integral operator. Conditions for the existence and uniqueness of a fixed point for the integral operator are derived viab-comparison functions on completeb-metric spaces. In addition, estimates for the convergence of the Picard iteration sequence are given. An estimate for the Green's function related with the problem is provided and employed in the proof of the existence and uniqueness theorem for the solution of the given problem. Illustrative examples are presented to support the theoretical results.
  • Article
    Citation - WoS: 54
    Citation - Scopus: 64
    F-Contraction Mappings on Metric-Like Spaces in Connection With Integral Equations on Time Scales
    (Springer-verlag Italia Srl, 2020-06-07) Agarwal, Ravi P.; Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.
    In this paper we investigate the existence and uniqueness of fixed points of certain (phi,F)-type contractions in the frame of metric-like spaces. As an application of the theorem we consider the existence and uniqueness of solutions of nonlinear Fredholm integral equations of the second kind on time scales. We also present a particular example which demonstrates our theoretical results.